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Computational OT #1 - Monge and Kantorovitch

Computational OT #1 - Monge and Kantorovitch

A course on computational optimal transport

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Gabriel Peyré

April 09, 2025
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  1. Theoretical Foundations Computational Optimal Transport Gabriel Peyré É C O

    L E N O R M A L E S U P É R I E U R E www.numerical-tours.com http://optimaltransport.github.io
  2. " Semi-discrete Optimal Transport ¸ = 3 ¸ = 50

    ¸ = 100 Matching Iterations of the semi-discrete OT algorithm minimizing (5.8) (here dient descent is used). The support (yj ) j of the discrete measure — is the red points, while the continuous measure – is the uniform measure The blue cells display the Laguerre partition (Lg(¸) (yj )) j where g ( ¸ ) is dual potential computed at iteration ¸. wton solver which is applied to sampling in computer graph- sed in [De Goes et al., 2012], see also [Lévy, 2015] for appli- -D volume and surface processing. An important area of ap- semi-discrete method is for the resolution of incompressible mic (Euler’s equations) using Lagrangian methods de Goes ], Gallouët and Mérigot [2017]. The semi-discrete OT solver ompressibility at each iteration by imposing that the (possi- d) points cloud approximates a uniform inside the domain. rgence (with linear rate) of damped Newton iterations is f (a, b) and s igure 6.1: Example of computation of W1(a, b) on a planar graph with uniform weights wi,j = 1. eft: potential f solution of (6.5) (increasing value from red to blue). The green color of the edges is oportional to |(Òf) i,j |. Right: flow s solution of (6.6), where bold black edges display non-zero si,j , hich saturate to wi,j = 1. These saturating flow edge on the right match the light green edge on the ft where |(Òf) i,j | = 1. 1. Algorithmic Foundations 2. Entropic Regularization 3. (Gradient) Flows in ML (to be or not to be a gradient field)
  3. www.numerical-tours.com Unbalanced Optimal Transport Optimal Transport with Linear Programming Semi-discrete

    Optimal Transport Entropic Regularization of Optimal Transport Advanced Topics on Sinkhorn Algorithm
  4. Comparing Distributions for Learning <latexit sha1_base64="vT0xGll5ZYO8gmdwavYy0Ckm65g=">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</latexit> ATAC-seq

  5. Parametric model: ✓ 7! ↵✓ <latexit 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<latexit 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<latexit

    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<latexit 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<latexit sha1_base64="YYkL6JTK2uYxh8MNcanIViL0GK4=">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</latexit> Observations: def. = 1 n Pn i=1 xi <latexit 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<latexit 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Comparing Distributions for Learning <latexit 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<latexit 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<latexit 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↵✓ <latexit 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ATAC-seq
  6. min ✓ D(↵✓, ) <latexit 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<latexit 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<latexit 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Density fitting: <latexit 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<latexit 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<latexit 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<latexit 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Parametric model: ✓ 7! ↵✓ <latexit 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<latexit 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<latexit sha1_base64="YYkL6JTK2uYxh8MNcanIViL0GK4=">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</latexit> Observations: def. = 1 n Pn i=1 xi <latexit 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<latexit 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Comparing Distributions for Learning <latexit 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<latexit 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<latexit 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↵✓ <latexit 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<latexit 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ATAC-seq
  7. Monge optimal matching: <latexit 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<latexit 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<latexit 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<latexit

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[Monge 1784] <latexit 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Monge’s Problem Points (xi)i, (yj)j Permutation: <latexit 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<latexit 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<latexit 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: {1, . . . , n} ! {1, . . . , n} <latexit 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<latexit 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<latexit 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D(X, Y ) = min n X i=1 d(xi, y (i) )
  8. Monge optimal matching: <latexit 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<latexit 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<latexit 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<latexit

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[Monge 1784] <latexit 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Monge’s Problem Points (xi)i, (yj)j Permutation: <latexit 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<latexit 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<latexit 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: {1, . . . , n} ! {1, . . . , n} <latexit 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<latexit 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D(X, Y ) = min n X i=1 d(xi, y (i) ) ! Seems intractable: n! possibilities. <latexit 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<latexit 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<latexit 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<latexit sha1_base64="xAfoQVY7WeuWfvbTW5Z5P5YLXic=">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</latexit> ! Di↵erent number of points?
  9. 1-D Optimal Transport x1 x2 x3 x4 x5 y1 y2

    y3 y4 y5 min 2⌃n n X i=1 |xi y (i) |p, p > 1 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  10. 1-D Optimal Transport xxx x1 x2 x3 x4 x5 y1

    y2 y3 y4 y5 min 2⌃n n X i=1 |xi y (i) |p, p > 1 <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="728Z8fBn49NzO1ft9oZkwnWJbMw=">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</latexit>
  11. 1-D Optimal Transport xxx x1 x2 x3 x4 x5 y1

    y2 y3 y4 y5 n n ! n(n-1)/2 n log(n) 10 3628800 45 23 11 39916800 55 26 12 479001600 66 30 25 1,551x1025 300 80 70 1,198x10100 21415 297 QuickSort: O(n log(n)). <latexit 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<latexit 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Sorting algorithms: insertion n(n 1)/2 worst case. <latexit 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<latexit 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<latexit 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min 2⌃n n X i=1 |xi y (i) |p, p > 1 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  12. 1-D OT Interpolation comparison <latexit 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<latexit 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<latexit 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Grades 1 <latexit 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<latexit 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<latexit 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Grades 2 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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0 10 20 x1 x2 x3 x4 x5 y4 y1 y5 y3 y2 Grades 1 <latexit 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<latexit 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Grades 2 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Grades /20 <latexit 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  13. 1-D OT Interpolation comparison <latexit 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<latexit 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<latexit 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Grades 1 <latexit 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<latexit 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<latexit 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Grades 2 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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0 10 20 x1 x2 x3 x4 x5 y4 y1 y5 y3 y2 Grades 1 <latexit 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<latexit 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Grades 2 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Grades /20 <latexit 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  14. Grayscale Histogram Equalization f[argsort(f.flatten())] = np.sort(g.flatten()) <latexit sha1_base64="XvM/j+TRFdrUIRjd7RjpxM4w5ws=">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</latexit> f

  15. Grayscale Histogram Equalization f[argsort(f.flatten())] = np.sort(g.flatten()) <latexit sha1_base64="XvM/j+TRFdrUIRjd7RjpxM4w5ws=">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</latexit> f

  16. In 2-D xi xj n = 10 n = 70

    n = 300 xi xj xj0 xi0 xi xj xj0 xi0 ci,j = ||xi yj || = q (x1 i y1 j )2 + (x2 i y2 j )2 xi, yj 2 R2 Proposition: two segments never cross. <latexit 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<latexit 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<latexit 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  17. Source image (X) Style image (Y) Sliced Wasserstein projection of

    image color statistics Y Source image after color tra Optimal transport framework Sliced Wasserstein projection Applications Application to Color Transfer Source image (X) Sliced Wasserstein projection image color statistics Y Optimal transport framework Sliced Wasserstein projection Applications Application to Color Transfer Source image (X) Style image (Y) Sliced Wasserstein projection of X to style image color statistics Y Source image after color transfer J. Rabin Wasserstein Regularization optimal In 3-D: Color Image Palette Equalization Reference <latexit 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sha1_base64="3GKcotffcbQ7ZK6RRi5K3JhAuCs=">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</latexit> Output <latexit 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<latexit 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<latexit 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<latexit 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Input <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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transport <latexit 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  18. Probability Measures d↵(x) = ⇢↵(x)dx 2.2. Assignment and Monge Problem

    9 Discrete d = 1 Discrete d = 2 Density d = 1 Density d = 2 Figure 2.1: Schematic display of discrete distributions – = q n i =1 ai”xi (red cor- responds to empirical uniform distribution ai = 1/n, and blue to arbitrary distri- butions) and densities d–(x) = fl– (x)dx (in violet), in both 1-D and 2-D. Discrete distributions in 1-D are displayed using vertical segments (with length equal to ai ) and in 2-D using point clouds (radius equal to ai ). is the dimension), can have a density d–(x) = fl – (x)dx w.r.t. the Lebesgue measure, often denoted fl – = d – d x , which means that ⁄ ⁄ ↵ = P i ai xi Positive Radon measure ↵ on a metric space X. X = Rd <latexit 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  19. Probability Measures d↵(x) = ⇢↵(x)dx 2.2. Assignment and Monge Problem

    9 Discrete d = 1 Discrete d = 2 Density d = 1 Density d = 2 Figure 2.1: Schematic display of discrete distributions – = q n i =1 ai”xi (red cor- responds to empirical uniform distribution ai = 1/n, and blue to arbitrary distri- butions) and densities d–(x) = fl– (x)dx (in violet), in both 1-D and 2-D. Discrete distributions in 1-D are displayed using vertical segments (with length equal to ai ) and in 2-D using point clouds (radius equal to ai ). is the dimension), can have a density d–(x) = fl – (x)dx w.r.t. the Lebesgue measure, often denoted fl – = d – d x , which means that ⁄ ⁄ ↵ = P i ai xi Positive Radon measure ↵ on a metric space X. X = Rd <latexit 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<latexit 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Probability (normalized) measure: ↵(X) = R X d↵(x) = 1 Integration against continuous functions: Measure of sets A ⇢ X: ↵(A) = R A d↵(x) > 0 R X g(x)d↵(x) > 0 d↵(x) = ⇢↵(x)dx ↵ = P i ai xi R X gd↵ = P i aig(xi)
  20. Push Forward ↵ T <latexit 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<latexit 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<latexit 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<latexit 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Push-forward: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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T]↵ <latexit 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Map: T : X ! Y <latexit 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<latexit 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<latexit 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P i xi 7 ! P i T (xi) <latexit 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<latexit 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P i ai xi 7 ! P i ai T (xi) <latexit 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<latexit 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x 7 ! T (x) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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8 < : <latexit 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<latexit 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<latexit 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<latexit 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  21. Push Forward ↵ T <latexit 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<latexit 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<latexit 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<latexit 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Push-forward: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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T]↵ <latexit 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Map: T : X ! Y <latexit 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<latexit 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<latexit 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P i xi 7 ! P i T (xi) <latexit 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<latexit 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P i ai xi 7 ! P i ai T (xi) <latexit 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<latexit 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x 7 ! T (x) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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8 < : <latexit 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<latexit 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<latexit 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seful for applica- mplex instead of rmance increase. on further speeds of the final trans- recision, but that polation scheme thod to generate the performance D image retrieval rs [Rubner et al. . 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<latexit 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y = T(x) <latexit 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<latexit 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<latexit sha1_base64="SLqhf2ynx7RkQrk5I2Me8kQffP0=">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</latexit> (T]↵)(E) def. = ↵(T 1(E)) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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General case: <latexit 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<latexit 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<latexit 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  22. Push Forward ↵ T <latexit 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<latexit 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<latexit 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<latexit 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Push-forward: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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T]↵ <latexit 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Map: T : X ! Y <latexit 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<latexit 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P i xi 7 ! P i T (xi) <latexit 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<latexit 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P i ai xi 7 ! P i ai T (xi) <latexit 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<latexit 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x 7 ! T (x) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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8 < : <latexit 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<latexit 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<latexit 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seful for applica- mplex instead of rmance increase. on further speeds of the final trans- recision, but that polation scheme thod to generate the performance D image retrieval rs [Rubner et al. . 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<latexit 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y = T(x) <latexit 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<latexit 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<latexit sha1_base64="SLqhf2ynx7RkQrk5I2Me8kQffP0=">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</latexit> (T]↵)(E) def. = ↵(T 1(E)) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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General case: <latexit 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<latexit 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Change of variables: <latexit 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= T]↵ <latexit 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PL3lt+dkyaVm7NeeJrtm42xl7UpnJAo+a1zlqY8nlovHBovAjUYYv2Gq0WTb2xRM/F2KKldytD+dXh1qpBeS5Slj0ygxoFSOnGUmFU+yJVOcY3qLcirU2RVgdmq7sb4M75EKR/rq/O7m/z1T1St8m36ZEHxvFLn2bpiHwuU1sdqTEF5HxD21d39repBrl3yYIiZT7HiTOGd516dJ3lkv5Sr2wp2XlrEcy5pVPdxtjYNpV/s4Y8oTkxpXlpEDeoRazld+WIVizSNcfniCjz3yGfiv2O6pjZbW3fSVTwJ2y8ybPK8uJIYUz6lzJv+2vR674Tv0YUE861d90FWvXfMFJgjMkk+D3LKb0hXOV4J4E92i7Zz3U7xbt4Y0eiayT1Uv0hwMZw1GvHuju2TI9N334FLVHr9q37Wsj8kmCOEr/z7Oh1aFU70T7qcuX+fLQ6epUr3lfpYb7C1+pjTm3cyMJGeUVMW30ezIUlqseFMSFc6vWijvz1JK8jM+9OhVI2rQ3lYqaBbcwxxUvSOVBE+Ly7K15v7lOhH901el3CutS4RqKE2bhU5wdcS4tZqWglQnLrpTUpcdajsvXC8nBXDWvH2VLGZAUTJeVuuLXbh3YhWpGzMUyhp/hkb1mc6NL8HC78HSlflGg4huQQm+Dn3lTbavcdnIp4pcuc2YyoBm1CfyUG7+h+FltU6+iVQ92lH8IhnMcIdC1JP6IVta7sTFmW3KUeTv+UrEGmYlF627J+H1wuck/WOdXpz4gsnNybkTLf5NTti+EQ0pMil3A+vL8h9WKgzLdN9fpgqMs9KHKow8OcZwh757Z1fV4up2p9rXMJ5cHrgNl5MTjcASyPWWy7EAuVOW/k3XNA6zCooG5Wi/+1H4aP5VSfVyi3KX1z9iLgrXO7WGdm0S+uP2cst5DRXM4xnGea9856TX5+7P9Ftd5U6vTm3dNHv9SOAcNrqTgfKkvHeHcUWXlDqeD+gE+GVP1T/eWC/FXCq5xGmRx1KJn9inJqpoVMzXx56eudeRYik6VTJlORmo0nmnQydlvtq9vws517gHVPifI3lfwXsf7vaPtQOyDrYbLpnEFoU11MWRC7m9ane3uOtkxiPNPLZ3xbUIN74g2qxfO+96g9nvltFfpW/iUJz/WvVKr6hchkdZfPzqsu9KC4A8e5IPO9b0Rn6jmbxSfQTgL2GPkcFUdK5uvnJSH6FBeuSrokhBktVZS7XspdOpMUl9DuFvrWoxE+0Tv9uO+A5/M7eXYpUr+muo5eHXClrtL6gf4OuCjTE8oLdEn7mxCf/VZdhb9Xddkv54GSc1Ctc3FrrfR/Sm+22M/XzrPq82Vn3tFmv5G8TNk1k/9b6HYp5QrsnmR1fnenlAufo6/GDyvwQ0fKJo2BlxTNZ6o6IzmvoDnXMrm7xGNlsqmsB4yRO/moq47KFxW8FgH9v1uKvutIugeydCmHH9EuYUb0Eq2bXZKeT2tWZ4PvVEhrvgVlmva8ph0H5uRl9U5D4h33rk3h05VSBiguoeNaED7nKZ1BGZ1z3k8Czlh0Anor9zWkpxKVuSjJPOD75kWALIsAOgNBmoFIYShKou3D80sbW6v/g8h64ej6ta3Na1sPbmx8cUv/7yIfqJ+rj9UVWFF/p76A8X+gDoHTG/VH9Sf1552/7vxr5987/+Gm713QmI9U4d/u+/8FCedXOg==</latexit> <latexit 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<latexit 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Densities d↵ dx = ⇢↵: <latexit 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<latexit 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sha1_base64="wKnxbOt7+IXe41dpkCS+2UP/V+A=">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</latexit> ⇢↵(x) = | det(@T(x))|⇢ (T(x)) <latexit 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<latexit 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R Y g(y)d (y) = R X g(T(x))d↵(x) <latexit 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vNcY72iEflJU02tT/5BdbbG9fmX1zHM2bzOY4RqSta3LacT52tZtUTGX0jAqk1qyoH+xdTxwYo0ZmpdjK9YhklhfV+mY9d41PwuaDGC2c97AFLOPAUJTU4CrXcKFNfEqKvYM4NbF3E4So4WUC1dOxG9RcuXs0bFukOqleIy21urxxbZ6zGNvSH5hLukWUkPu6VvuIyipKHdgoZkenV091HP16L2V0XccAExzEdah3aEeCetOk71ab3h6PiK3uWZwMV7Pnb8Yrb5SFsbjHkyskUoSxVPt53JI7l1uK5eVzbHzc8ieqNor07IavRpR2osRqEmW8ze+IzuLe192pNDHkyjA+8x0lSGinfNMIuO+fSILKprbyXeqC+ToePymKyuscfV6J6D7nnQ9WOcDVgxHkGpCTHDPtw1A6Kci7muMtL4SP0h3x3N6A1WR/RpwUIaGmxvkoKFrIqy3xSofAA0jgaO0sNpLNIx+NYSJTnq98ljY9ei5b9CO7dmf7tNY7x8NJdnYrrEdZ24RjRreFeX7xY5sAQz75N18l+re4n86nBEGypxfe1wZr0MaMc/oQh2SJ5xSrNNmh3F1m5+avGJ4bSnzN457mZnZCEjsn8RrE8ZjcmIftyzA2YHnS1CSjYyxO70c+/G5+v0xTFm/bi+4lMNdrwlZMumxN/QdWfXmMYiRwy8DswXxrbRyS75gglxHWnrbud29eqDSHtOwh0lTNGOlavE/xr9Nj9mnKwsjQjUML6BsbZ1vveRUcyCOmrTKl9tg0xbV8rLuQyvtdR2/bMyXS5ItkkRF8qDq3UXOHfonnnhKBmR3OOlNryOVmVzkfJwQY/Y2yOK4tnu9/QKjHJfp1VyheZci0ZJD0bBJI8iTFspi7zIt5pXkXoY7fH/hbrVdVFrSDFSNoPLGpLy+wlFa66UKYxqHr/vaDb5tT5aaFXNZ0Bj8diZy99B7W/ht5Hb3IfRiQtW4S6NAaZg76xGuCZaahHG626BlxmZhpa9t/zsmDSt3JrzxNds3WyMfVKbyh6NmlOdtTDl89B469B4G6jDJu01Wi2aemOJDsXYoql3K0P51eHWrEF5KlKWPTKD6gdI6cZSYVS7IlU5xjeojyKtVZFWG2aruxvgzvkQpH+uL87u7/LVPVL3yLfpkAfG8UuXZmmffC5TWx2pMQXkfFPbV3f2t6gGucdkQZEyn+PEGcO7Th265rmkv9MrW0Z23loEc27pg25jbGyLyn9aQh7TnBjTvDSIm9Qi0fK7ckQLFumG43NElPlvk0/Ffkd1zOy2tu8kKvgTNt7kWWV5caQwIP1Lmbedpeh1x4lfI4oJp9q7joFW/TeMFBhjMgl+z3JMbwhXOd5JYI82Jvu5bKd4F2/gSHSDpJ6p2wE2hqNeO9bdsWV6bPr2e2iJWrdv3ddC5pcGc5T4nWdHr02r2rH2UWcL9+ej1darXPG+Sg/TBb5WH1Nq40YWNsorYlrqVjAXlqgeF8aEcKnXizry15O8jsy8OxVK2bQ2lIuZBrYxbyheks6BIsLn3V31enPXhH7ES/RiwrrUuEaihNm4TOcHXEuLWaloIUJy66U1KXXWo7L1wvJwVw1rx9lSJmQFUyXlbri124dWIVqRszFMoaP4ZG9ZnOjSvAUX/o6UL0o0HENyiA3wc++oDbX1CU5FvNdlzmxGVIM2obsQg7d1P4stqnX03qHu0g/hEM6jD7qWpO/TilpXdqYsS+5SD6f/gazBSCWi9LZl/T64XOSeLHOq058+WTi5N31lvsmp2xfDIaQnRS7hfHh/Q+rFkTLfNtXrg6Eu96DIoQ4Pc54h7J3b1vV5uZyq9bXMJZQHrwNm58XgcAewPGax7UIs1Mh5I5+eA1qHowrqZrX4X/th+FhO9XmFchvTN2dvA946t0t0Zhb94vpzxnILGc3lHMN5ZnnvrNfk58f+X1TrTWVObz49ffRL7RgwvGaK86GydIx3R5GVN5QK7g/4ZMjUf9TfL8hfJbzPaZTJUYeS2a8op2ZayNTMl5e+3plnITJZOmUyFanZeKJBJ2M31I66Bz8buQdY95Qof1PJfxHr/462C7VHZD1MNp0zCC2qSygLYnfTunRvz9GWSYxnevmMbxNqcE98l2rxvO8jao9nfpuFvpV/ScJz/aHKVLcQmSzu8tl5FUMPijtwnAsy3/tGdKaes1l8Au04YI+Rz1FxpGS+fp4Roktx4aKkM0KY0VJFOfZSjulMUlJCOy70rUMjfKh3+nHfAc/nt/PsUqT+SHVtvTrgSl2l9T39HXBRppeUF4hJ+6sQn/1ZXYe/13XZL+eeknNQzXNxay70f0xvttjPU+dZ9fmyuXe02W8kr1B2zeT/TnS7jHIFdk+yOr+7WcqFz9FX43sV+J4jZYPGwDuK5keqOiM5raA51TK5u8QDZbKprAeMkdv5qKuOyk8qeJ0E9P9BKfqBI+k2yBJTDj+iXcIR0Uu1brZIej6tWZ0Nvl8hrfkWlGna85p2HJiTl9U7Dal33Ls2hU9XShmgpISOa0H4nKd0BqV/znk/DDhj0Q7ordzXkJ5KVKaiJNOA75tPAmQ5CaBzJEhzJFLoiZJo+3B4aWVt8X8QWS4crN9YW72x9mR95eu7+n8X+Vz9Rn2lrsKK+hf1NYz/PbUPnP6m/qm+V//e+mLr5tatrdvc9LMLGvNrVfi3de+/u9Rq9A==</latexit>
  23. Random vectors Radon measures P(X 2 A) = P(Xn 2

    A) n!+1 ! P(X 2 A) 8 set A 8 continuous function f Weak⇤ convergence: Convergence in law: Measures and Random Variables R A d↵(x) R fd↵n n!+1 ! R fd↵ Weak convergence: . . . ↵1 ↵2 ↵3 ↵ . . . Push-forward: X ∼ α T(X) ∼ T♯ α T]↵ <latexit 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↵ T <latexit 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  24. Continuous Monge’s Problem ↵ Y <latexit 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<latexit sha1_base64="V/ijx18qSlgI3jCwJ6JJh1g2VwY=">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</latexit> <latexit

    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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Gaspard Monge T <latexit 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<latexit 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<latexit 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inf =T ]↵ Z X c(x, T(x))d↵(x) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  25. Continuous Monge’s Problem ↵ Y <latexit 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<latexit sha1_base64="V/ijx18qSlgI3jCwJ6JJh1g2VwY=">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</latexit> <latexit

    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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Gaspard Monge T <latexit 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<latexit 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<latexit 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Discrete case: <latexit 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<latexit 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<latexit sha1_base64="q7OQYOXIvuTuAKQi9e1ICZoeO5Y=">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</latexit> ↵ = Pn i=1 xi <latexit 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<latexit 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<latexit 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= Pn j=1 yj <latexit 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<latexit 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<latexit 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<latexit sha1_base64="B0/7Q0xaRpkid90QuR/UJOBxWDQ=">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</latexit> Ci,j = c(xi, yj) <latexit 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<latexit 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min 2⌃n n X i=1 Ci, (i) <latexit 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<latexit sha1_base64="9c50g6gbnvG3Zcd4CgGqg0hmEvc=">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</latexit> inf =T ]↵ Z X c(x, T(x))d↵(x) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="H4SzjqeKxRpGkCl+FqrHBNnEXiQ=">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</latexit>
  26. Continuous Monge’s Problem ↵ Y <latexit 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<latexit sha1_base64="V/ijx18qSlgI3jCwJ6JJh1g2VwY=">AAA9inictVttcxu3EYbTl8Rq0zjpx850rlXcSTquRlI802Y8mon1YkmxYskmJdsJbQ1fTtTZJx7NIyXLjH5Jv7a/o7+j/6D91L/Q3QVwwJG4W0B1dSMJB+J5drEHLHaBY2eYJvl4efmfNz74yU9/9vMPP7q58ItffvyrT259+tlRnk1G3fiwm6XZ6FmnncdpMogPx8k4jZ8NR3H7rJPGTzuvN/Dzp+fxKE+yQXN8OYxfnLX7g+Qk6bbHUHV865MWcUw76SS+aj2/PL61uLy0TD/RfGFFFRaF+jnIPv3tqmiJnshEV0zEmYjFQIyhnIq2yOH6QayIZTGEuhdiCnUjKCX0eSyuxAJgJ9AqhhZtqH0Nf/tw94OqHcA9cuaE7oKUFH5HgIzEbcBk0G4EZZQW0ecTYsbaKu4pcaJul/C/o7jOoHYsTqGWw+mWvjjsy1iciL9QHxLo05BqsHddxTIhq6DmkdWrMTAMoQ7LPfh8BOUuIbWdI8Lk1He0bZs+/xe1xFq876q2E/Fv0vI2XJFoqN5nBUNbnBN/RE9zAp9JfVKQ3AeGWPURSxdk6zPq/QDaT6H+EVxXVNI26cA1pdqrWuQGXC7kBovchsuF3GaRe3C5kHss8gAuF/JAIRE7Ipu78Q24XPgGK/kxXC7kYxb5BC4X8gmLPILLhTxikd/D5UJ+zyIfwOVCPmCRD+FyIR+yyCZcLmSTRR7C5UIessgtuFzILYWsnqkjuDLiSZhZeR/KZRnoKVKouc/qt07e0YVd95jT3QosP6s34b8bu+lh07gCu+Ux7k4qsPzI2wYf6cbyvmiHVhMXdofF7sIIcGN3Wey34lUF9luPmfa6AsvPtT1o58by3vc7uHNjv2Oxj6DkxvJr1D7UuLH7HivGsAJ7wGIfizcVWB+vP6rA8n6/AX7FjeXXqSa0d2N9vOmkAsv70yOIYNxYfrV6CrVu7FMW+0y8rcA+Y7HPwbu7sc89Vth3FVi9xi7QCtKneCSGGVvH1i5mJZaGwNZm5KfF2pJSbNyBeg7TLzB9wpyxiO0Cse2J2CsQe9565YUfzSne5aU0CkTDE9Ep1iYsjdn2vaI9llIPxGaB2JxB1EWk+Kx1X84putA1HHJcrFxY8ulTVvhvLMVqPNR7Xo3YLyHk2D6lkX+HsiXMoNBSdWynxRovkRHd1yEuKHvTvdQyeNy48Ao26i2L6jhQHRZ16UBdsqiJAzVhUecO1DmLMjPfxrU8RoCxPz6LKd3JESBj5OorgqjgPqw6OzBHIxg/BxAFPqGaffjfoNybu+o0w2we10nc5XhR8sQjKE3FItSbrHCT8uuUZlgMmsmW+yrHxzvc25iqOSe98FWxkkfFjok/T0L69AsejBYjmk9hPA+p5oqiO1kKw+8U816XwvBbZPEriuJlKQw/VtqPr6F7U2Gb18A2YDYNlfVNOZRD7r9IDl1eoFUXPS4+1TM1ZpDvbSD/rnoyu9d4LhtUkvYx5TCO3OpfXupfCIexc27ZOYwFoycZ9epSFNyTgcp7TTlUh4xW0YHSw9yFPhls01NPRpfDOA4g4tqgnHtqlUNH77DojSmHcRwJue95RZG8Lodx9Ole2sOUwzhwt6Wt8nxTDvXsaAGZO5tyqFcf0C4w7gHJMS9rTFQ0ojhpotgSig/qd2vsmH9+HcM9m5dFjlDPZGLbap5OsZbVa6TjhRi82jhQD4wvJlYMVuaYilU2v5I6jEvr+zyPWePR8ntgxQhmvzwD4PbMU9BQ70mg906BcYXNuso907hVFoej5GQG1VK1YzZaNHLlrlG57phqubzM9NbYsUX+OqexN6SYcI8sy9lhr/IJVzFyFtorWYjnC7HdOzVfy9ZfZnHDGcSwGGldOhGSJ2n1earL6g3LxrfVKc8YLnnmY8Yv7jafKG+DOU9Gvgh1qZNpt9P7SHYdrqt3hNnjlp9F9ETRX52T10joRCpns1C9Wyyj8SndG+5DOpNDGZKjC88xUixDIU/NcBcd99Mj8qi2v+Vko730Dp0s5+R1tT+uR/ctdN+BDs9xNmDFeASlJuQMh3DX9MhyFgpbZWTxkfhTcTqa0ROsz+jTkofUHNLfxCUPWZdln5ZYLgCNo0Fm6f4cszwa35pj4rN+lz4mdy17/tt0cqvPt9s0xqtHc/VOTI+krpLUiGaNPNWVd7MSpAZT5yerFL/W9xLlhUhEH8pJfWlJlnYZ0Il/TBnskCLjlGYbNzvKre39qdlPtKQDoc/O8TQ7Iw8Zkf+LYH3KaExG9Gu/O6BP0KVHSMlH+vidpIhuXLFOwo4xE8clQr7VYMZbTL5sQvI1rz27chqLMmOQ68DVzNjWNtmjWDAmqSPl3c3crl99EGnek7BHiWQ0Y+ULkv8l/dW/epwszo0ItDA+gVz5OtfzyChnQRu1aZWv90G6ra3l54UOL5XWZv0zOn1e0myTMi7UB1frHkju0r2UhaNkRHrnc23kOlq3m4vMwxk7Ym9PKIuXfr+vVmDU+w6tkos051o0SvowCsZFFqHbcrvIs3LrZZXZ/bjz/wu7sXXZasgYCbODKy3E7e/HlK3ZWqYwquX4fU2zyW310UyrejkDGotn1lz+EWp/B3+13vrej6dT8grrNAYkg7kzFpE10VwLP1nrJVl6ZGouc2/kmTGpW9k118mvpXczOfZ5MMsBjZq3atdCl6/D8crieOVpwyadNRor6nrtiY7Z3KKpTit95YVIawYwT1hmPiLTqMRDSzuX8mPtsax8jq9R71iuZZarDbPVPg2w57wP0j3XZ2f3j8XqHokHFNt0KQKT+UuPZmlCMZeurc/UJANKvqv8qz37W1SD0jvkQZFZvseJM0aeOnXpuio0/YNa2TLy88Yj6PeWLlQb7WNbVP5qDnlGcyKneakRd6lFrPS39YhmPNKSFXNEtPPfpphKxh31ObPd2jyTqBRPmHxTziojS2YKA7I/t/O2O5e97lr5a0Q54URF1x3gCn/CyCAxeifBHVnm9IRwlZMnCTKi7ZD/nPdT8hRvYGm0RFpPxZqHj5FZrxnr9tjSPdZ9+yO0RKubp+5qwctLvSVy8q5zotemVe1MxajTmfvrcbXVKle+r7PDZEausceE2tiZhcnyypiWuOctRWoUJkVifKSE9SJE/zDNQ3SWp1O+zLq1Zi7vNEgfc0r5EvceKCJc0d0XzmjuS6YfnTm+DmFtNlnDMeFuXKb2B2xPi7tSN+fWIVl7s3Y1Sq2VqGql0Oz2amH8t/SQMXm/VHB7NrK1rXurlKXwuzCSoSvkG71V+aHNeQ8u/BsJV3aoJfrsHTYgvr0vNsTWe3gb4o0qyx3NiGrQF/Rmcu+26me5Rb2N3ljsNr+PBH8ZCdia0z6hlTRUd8nMa26z+/NfkBcYiZjV3rQM74Mthe/JvKSQ/iTk2fjeJEJ/Fye0L1qCT0/KUvzlyHMNrhcnQn+nKawPmp3vQVlCiAz9HoPfMzetw2XZkurtNS/FV4ZcBfSJi8bhyV91rmLa+XiokfVE3r8E9A4nNex6tfhf+6HlGEnhsnyl5fRds1ceT122i9WOLMbD4XPGSPMZzdUS/WVmRe9MtOSWJ+O+KOhJZVZv3j8/xqNmDGhZUyH3QXntJN4eRUZfXxY8F3DpkIn/iH/c4L+N8KbgqNIjhEmfU1Sz6RY8m/7Gpat3+jMfnQxPlU5lNpNHNOiN2A2xKx7A70YRAYa+HSq/Syn/I9b9/dke1J6Q99C76HLnoEV1Me1+mFO0Ht2rPcbjW4srs99Cni8cri59vbTy+O7iN+vqC8ofid+I30NasiL+LL4RO9DdQ4FfVP6r+Jv4+9rHa1+tfb12Tzb94IbC/FqUftY2/wuFudpq</latexit> <latexit

    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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Gaspard Monge T <latexit 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<latexit 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<latexit 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Discrete case: <latexit 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<latexit 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<latexit sha1_base64="q7OQYOXIvuTuAKQi9e1ICZoeO5Y=">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</latexit> ↵ = Pn i=1 xi <latexit 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<latexit 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<latexit 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= Pn j=1 yj <latexit 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<latexit 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<latexit 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<latexit sha1_base64="B0/7Q0xaRpkid90QuR/UJOBxWDQ=">AABFgnictVxfc9u4EUeu1/aa/su1j31hz0knd5NLbd912um1M5fYjuPESZRIdnIXJR5SohUmlKiIkuJEp+/Ub9Bv0Zk+tY/tU79CF7sAAUogF3TTcGyDIH67iyWw2F2AicZpkk83N/9+4YPvffj9H/zwox9d/PFPfvqzn1/6+BfHeTab9OKjXpZmkydRmMdpMoqPpsk0jZ+MJ3E4jNL4cfRqRz5/PI8neZKNOtO34/jZMByMktOkF06h6uTSncvdzk7wx2DRRVqLSdxfnp0ky6CbZqPBMBzn06x4GKWzePl2ebLo5slVG5EsP11ePrm0sXl9E/8F64UtVdgQ6l8r+/iTS6Ir+iITPTETQxGLkZhCORWhyOF6KrbEphhD3TOxgLoJlBJ8HouluAjYGbSKoUUIta/g9wDunqraEdxLmjmie8AlhZ8JIANxBTAZtJtAWXIL8PkMKcvaKtoLpCllewt/I0VrCLVT8QJqOZxu6YuTfZmKU/EH7EMCfRpjjexdT1GZoVak5IHVqylQGEOdLPfh+QTKPURqPQeIybHvUrchPv8XtpS18r6n2s7Ev1HKK3AFoq16nxUUQjFH+gG+zRk8I3lS4DwACrHqoyy9QV0PsfcjaL+A+vtwLbGkdRLBtcDaZS1yBy4XcodF7sPlQu6zyEO4XMhDFtmCy4VsKaTETlDnbnwbLhe+zXJ+CJcL+ZBFPoLLhXzEIo/hciGPWeS3cLmQ37LIW3C5kLdY5F24XMi7LLIDlwvZYZFHcLmQRyxyDy4Xck8hq2fqBK4M6STMrLwB5TIPaSlSqLnByncTraMLe9NjTvcqsPys3oW/buyuh07jCuyex7g7rcDyI28fbKQby9ui27iauLC3WewBjAA39oDF3hEvK7B3PGbaqwosP9cOoZ0by1vfe3Dnxt5jsfeh5Mbya9QDqHFjH3isGOMKbIvFPhSvK7A+Vn9SgeXtfhvsihvLr1MdaO/G+ljTWQWWt6fH4MG4sfxq9Rhq3djHLPaJOKvAPmGx34B1d2O/8Vhh31Vg9Rp7EVeQAfojMczYOmphMStlaQzUQoZ/WqwtKfrGEdRzmEGBGSBmyCL2C8S+J+KwQBx6y5UXdjRHf5fn0i4QbU9EVKxNsjRl2/eL9rKUeiB2C8TuCqLOI5XvWvdljt6FruGQ02LlkiWfPmWF/ZalWI2HesurEQ9KCBrbL3DkX8NoSUZQUlN11F4UazwhA7yvQ7zB6E33UvPgcdPCKtioMxYVOVARi3rrQL1lUTMHasai5g7UnEWZmW/juh4jwOhfvosF3tEIIB+5+grAK7gBq85tmKMBjJ8WeIGPsOYB/G1j7M1ddZLJaF6ukzLL8axkiSdQWogNqDdR4S7G1ynOsBgko5YPVIwv72RuY6HmHFnhZbGSB0XGxJ9OgvIMCjrSWwxwPjWjcxdrlujdUakZ/nYx73WpGX4PNb5EL55KzfBTJf30HLJ3FLZzDmwbZtNYad+Um9Kg/AvR0OWLuOpKiyvf6lCNGUnvrCH9A/VmDs7xXnawRPox5WY0cqt/eal/TWgYPeeWnptRkd4Teb26FDTuyUjFvabcVIYMV9GRksPcNX0zsk1fvRldbkajBR7XDsbcC6vcdPSOi96YcjMax4Lynkv05HW5GY0B3pM+TLkZDZltCVWcb8pNLbvUAMXOptzUqo8wCyxzQDTmqcZ4RRP0k2aKWoL+QX22xvb519cxmbN5XsQI9ZSMb1tNJyrWsnqJtL8Qg1WbNpRD+hczywcr01iIbTa+IhmmpfV9nY5Z46XmD0GLAcx+2gPgcuYpSKhzEtJ6p0Bxi426yj3TuG0WJ0fJ6Qqqq2qnrLdo+FLWqFx3grVcXGZ6a/TYRXud49gbo094iJrl9HBY+YarKHIaOixpiKfXRHfv1Hwta3+TxY1XEONipPVwR4h20urjVJfW25aOr6hdnilctOdjxq/MNp8qayNjngxtkZSljqfdTueR7Dq5rl4TJsdNzwJ8o9JezdFqJLgjlbNRqM4Wkze+wHtD+wj35CQPotGD9xgoKmNBu2Yyiy7z6QFaVNvecrylvnSGjso5Wl1tj+vRAws9cKCbxzg7sGLch1IHYoYjuOt4RDkXC11lqPGJ+LzYHc3wDdZH9GnJQmoaZG/ikoWsi7JflKi8AbQcDRSl+9NYpaPx3TVKfNTvksfErmXLfwV3bvX+dohjvHo0V2di+sh1G7kGOGtoV5fuVjmQBAvnk230X+t7Kfk14ShtKMf1ucWZ9DLCHf8YI9gxesYpzjZudpRb2/mp1SeaU0vovXO5m52hhQzQ/gWwPmU4JgP8sc8O6B10sggp2kgfu5MU3o3L10nYMWb8uETQqQYz3mK0ZTPkr+nasyvHsUgRA60Dy5WxrXVyiL5gjFwnyrqbuV2/+kikOSdhjxKiaMbKVeT/Kf7WP3qcbKyNCKlh+QZyZetc7yPDmEXqKMRVvt4G6ba2lJcLGZ4rqc36Z2S6XJJsFyMuKY9crfvAuYf3xEuOkgnKna+1oXW0LpsrKY9X9Ch7e4pRPNn9gVqBpdzXcJXcwDnXxVEygFEwLaII3ZbLIq/yredVpu5HO/+/UDe6LmtNUgyEyeCShrj8fozRmi1lCqOaxu8rnE1urU9WWtXzGeFYHFpz+Tuo/TX81nLrez86Uckq3MQxQBTMndEI1QRrLfx43Szx0iNT0zL3hp8Zk7qVXXOe+Jqsm4mx542ptHDUnKmshS6fh8ZLi8ZLTx12cK/RaFHXa0t0wsYWHbVb6cuvCbdOA8ozljLvkWlU4iGlHUv5Ue2zVPkYX6PesbQ2WVohzFZ7N8Ce8z5I91xfnd3fFat7IG6hb9NDD4zilz7O0gR9Ll1bH6kRBcn5S2Vf7dnfxRrJPUILKinTOU45Y2jXqYfXspD0N2ply9DOG4ugzy29UW20je1i+Ys15BDnRI7zUiO+xBaxkt+WI1ixSNctnyPAzH+IPhX5HfUxs93avJOg5E+YeJNmleFFkcII9c9l3g7WotcDK34NMCacKe86AlrN37CkQBidSXB7ljm+IbnK0U4CebQR2s91O0W7eCNLouso9UL82cPGUNRrxro9tnSPdd8+g5ZS6+atu1rw/FJvjhy/8+zohbiqDZWPuli5Px+tUK1y5fs6PcxW+Bp9zLCNHVmYKK+M6YqvvLmQRM24EMaHS7NeNJG/meRNZKbdKV/KurWmXM40kI15gfESdw5UIlze3VWnN/cp049ojV6EWJsa1XCUZDYuU/kB29LKrFSwEiHZ9dyalFrrUdV6YXjYq4ax42QpY7SCqeByN9Ta7kO3FK3w2Rii0BN0srcqTrRpfgWX/B0IV5SoOfrkENvg594QO2LvPZyKeK3KlNkMsEbahP5KDB6qfpZb1OvotUXdpu/DwZ9HArrmpE9wRW0qO1HmJbep+9N/g9ZgImJWetOyeR9sLnxP1jk16U+CFo7vTSL0NzlN+6I5+PSkzMWfD+1vcL04FfrbpmZ90NT5HpQ5NOGhzzP4vXPTujkvm1O9vta5+PKgdUDvvGic3AGsjllMOx8LNbHeyPvnIK3DaQ11vVr8r/3QfAyn5rx8ueX4zdlLj7dO7WKVmZV+cfM5Y7j5jOZqjv48s6J3xmty8yP/L2j0pjKrN++fvvRLzRjQvBaC8qG8dIS3R5GR15eK3B9wyZCJ/4i/XuC/Snhd0KiSowklvV9RTU234KnpLy9dvdPPfGQydKpkKlMz8UQbT8buiANxC352Cg+w6SlR+qaS/kqs+zvaPtSeovXQ2XTKIHSxLsYsiNlN6+O9OUdbJbE800tnfDtQI/fED7FWnve9j+3lmd9OqW/VX5LQXL8nMtEvRSaru3xmXkXQg/IOHOWC9Pe+AZ6pp2wWnUAbeuwx0jkqipT0188LRPQxLlyVdIEIPVrqKEdOyhGeSYoraEelvvVwhI/VTr/cd5Dn88MiuxSI32JdqFYHuVLXab2lvgMuy/QU8wIRan8T4rPfiWvw95oqu+VsCT4H1TkXt85K/3N8s+V+nlnP6s+XLZ2jzXwjeQWzazr/N1ftMswVmD3J+vzubiUXOkdfjx/U4AeWlG0cA68wmp+I+ozkrIbmTMlk7xKPhM6mkh5kjBwWo64+Kp/X8Jp79P9uJfquJek+yBJhDj/AXcIJ0kuVbvZQejqtWZ8Nvl0jrf4WlGia85pmHOiTl/U7Dalz3Ns2hU5XchmguIKObUHonCd3BiU557wfe5yxCD16y/fVp6cclRkryczj++a5hyxzDzqnjDSnLIUBK4myDyeXNrZW/weR9cLx9vWtzetbD7c3vr6p/neRj8SvxCfiKqyovxdfw/hviSPg9BfxN/EP8c+9D/c+29va+4KafnBBYX4pSv/2/vRfQhxqeA==</latexit> Ci,j = c(xi, yj) <latexit 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<latexit 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min 2⌃n n X i=1 Ci, (i) <latexit 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<latexit sha1_base64="9c50g6gbnvG3Zcd4CgGqg0hmEvc=">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</latexit> inf =T ]↵ Z X c(x, T(x))d↵(x) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="H4SzjqeKxRpGkCl+FqrHBNnEXiQ=">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</latexit> ? ↵ ↵ ↵ ↵ Non-symmetry, non-existence, non-uniqueness: <latexit 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<latexit 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<latexit 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↵
  27. Brenier’s Theorem Hypotheses: <latexit sha1_base64="Kz6oWTOyZxQfM22h7hulfw17JC4=">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</latexit> <latexit 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<latexit 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<latexit

    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<latexit sha1_base64="Kz6oWTOyZxQfM22h7hulfw17JC4=">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</latexit> c(x, y) = ||x y||2 <latexit 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<latexit 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<latexit sha1_base64="8N+YrFgHwCNqJVdrD67sfxTeobw=">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</latexit> d↵ dx = ⇢↵ density. <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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↵ <latexit 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<latexit 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W2 2 (↵, ) def. = inf =T ]↵ Z Rd ||x T(x)||2d↵(x) <latexit 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<latexit 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<latexit 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<latexit 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X = Rd <latexit 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<latexit 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<latexit sha1_base64="XN+iO57sWsbXjQR+wAEZLNcSmm8=">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</latexit>
  28. Brenier’s Theorem Hypotheses: <latexit sha1_base64="Kz6oWTOyZxQfM22h7hulfw17JC4=">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</latexit> <latexit 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<latexit 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<latexit

    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<latexit sha1_base64="Kz6oWTOyZxQfM22h7hulfw17JC4=">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</latexit> c(x, y) = ||x y||2 <latexit 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<latexit 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<latexit sha1_base64="8N+YrFgHwCNqJVdrD67sfxTeobw=">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</latexit> d↵ dx = ⇢↵ density. <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Yann Brenier There exists a unique Monge map T. <latexit 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<latexit 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<latexit sha1_base64="nsglRAUi+tlHeI1cLZ6LHMM7xpo=">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</latexit> It is the unique T = r' such that <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="jRX8giyUu12rfn1251pXgPCW+54=">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</latexit> ' is convex and (r')]↵ = . <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="tvjr0hwMzBZ6qILEwzAGLTMLlqQ=">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</latexit> Theorem: [Brenier, 1991] <latexit 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<latexit 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↵ <latexit 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<latexit 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W2 2 (↵, ) def. = inf =T ]↵ Z Rd ||x T(x)||2d↵(x) <latexit 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<latexit 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<latexit 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<latexit 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X = Rd <latexit 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<latexit 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<latexit sha1_base64="XN+iO57sWsbXjQR+wAEZLNcSmm8=">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</latexit>
  29. Brenier’s Theorem Hypotheses: <latexit sha1_base64="Kz6oWTOyZxQfM22h7hulfw17JC4=">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</latexit> <latexit 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<latexit 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<latexit

    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<latexit sha1_base64="Kz6oWTOyZxQfM22h7hulfw17JC4=">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</latexit> c(x, y) = ||x y||2 <latexit 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<latexit 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<latexit sha1_base64="8N+YrFgHwCNqJVdrD67sfxTeobw=">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</latexit> d↵ dx = ⇢↵ density. <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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! Monge-Amp` ere equation (non-linear, degenerate elliptic). <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="vq9eQR/Pj8oaAYzIMN53xm+UT20=">AAA9xXictVttcxS5ERaXt4O8ccnHVKUmMaQgBS7buaokdeWqAxuwwYBh14a7WyD7Ml4PzO4ss7M2sOfKX8o/yL9IVT4lH5NP+Qvpbkkjza5mWnKIVbY1Wj3drZbUL9Jsb5Im02Jt7e8XPvnOd7/3/R98evHSD3/045/89PJnPzucZrO8Hx/0szTLn/e60zhNxvFBkRRp/HySx91RL42f9d5s4efPTuJ8mmTjdvF+Er8YdYfj5CjpdwtoenX5/pVOngyPi26eZ6dXovnDbDyMb94aTTp/ivM4it/OqGN0bZyNbyKTbn4jGsTDeBzn3QI6pGkyKZL+9dWzV5dX1lbX6CdarqyryopQP/vZZ7/cEB0xEJnoi5kYiViMRQH1VHTFFMo3Yl2siQm0vRBzaMuhltDnsTgTlwA7g14x9OhC6xv4O4Snb1TrGJ6R5pTQfeCSwm8OyEhcBUwG/XKoI7eIPp8RZWytoz0nmijbe/jfU7RG0FqIY2jlcLqnLw7HUogj8QcaQwJjmlALjq6vqMxIKyh5ZI2qAAoTaMP6AD7Pod4npNZzRJgpjR1126XP/0U9sRWf+6rvTPybpLwKJRItNfqspNAVJ0Q/otmcwWdSnhQ4D4FCrMaItVPS9YhGP4b+c2h/BOWMalonPShzaj1rRG5BcSG3WOQ9KC7kPRa5B8WF3GOR+1BcyH2FRGxOOnfjW1Bc+BbL+QkUF/IJi3wKxYV8yiIPobiQhyzyaygu5Ncs8i4UF/Iui3wAxYV8wCLbUFzINos8gOJCHrDIO1BcyDsKWb9TcygZ0UmYXXkL6lUeaClSaLnFynebrKMLe9tjT/drsPyu3ob/buy2h07jGuwdj3V3VIPlV949sJFuLG+LdsibuLA7LHYXVoAbu8ti74vXNdj7HjvtTQ2W32t70M+N5a3vQ3hyYx+y2EdQc2N5H/UYWtzYxx4eY1KD3WexT8TbGqyP1c9rsLzdb4FdcWN5P9WG/m6sjzWd1WB5e3oIEYwby3urZ9Dqxj5jsc/Fuxrscxb7FVh3N/YrDw/7oQarfewl8iBDikdi2LFN1LrlrsTaBKh1Gf5p6VtSio170M5hhiVmSJgRi7hXIu55IvZKxJ63XNPSjk4p3uW5tEpEyxPRK30T1gq2/6Dsj7XUA7FdIrYXEE0RKc61HssJRRe6hUMWpefCms+YstJ+Yy1W66HZ8mrE4wpCru1jWvk3KFvCDAo11UTtuPTxEhnRcxPilLI3PUrNg8cVpVWwUe9YVM+B6rGo9w7UexY1c6BmLOrEgTphUWbn27iOxwow+se5mNOTXAEyRq4vEUQFt8Dr7MAejWD97EMU+JRaHsP/FuXeXGmSDLN59JN4yvGiYolzqM3FCrSbrHCb8uuUdlgMksmej1WOj094tjFXe05a4bPSk0fliYk/nYTkGZZ0MFqMaD+F0XlALWcU3claGH6n3Pe6Foa/Qxo/oyhe1sLwhZK+OIfsbYVtnwPbgt00Udo39VAa8vxF0tD1S+R10eLirI7UmkF67wLp76qZ2T3HvGxRTerH1MNoTK3xTSvjC6Fh9Dy19BxGBaMnGfXqWhQ8krHKe009VIaMvOhYyWGeQmcG+wzUzOh6GI19iLi2KOeeW/XQ1TspR2PqYTQOhTz3PKNIXtfDaAzpWerD1MNo4GlLV+X5ph5q2VEDMnc29VCrPqZTYDwDkmtetpioKKc4aaaoJRQfNJ/W2DH/sh/DM5uXZY7QTMnEtvV0eqUva5ZIxwsxWLUiUA6ML2ZWDFalMRcbbH4lZSgq/n2ZjvHxqPk90GIEu1/eAXBn5ilIqM8k0HqnQHGdzbqqI9O4DRaHq+RoAdVRrQUbLRq+8tSo2vaKWrm8zIzW6LFD9npKa29CMeEeaZbTw17tDNdR5DS0V9EQTy9Edx/Ufq1qf43FTRYQk3Kl9elGSN6kNeepLq23LB1fVbc8BRR552PWL542HylrgzlPRrYIZWniaffT50h2G/rVG8KcccvPIppRtFcnZDUSupGaslmoPi2W0ficng3tA7qTQx6SRh/mMVJUJkLemuEpOp6nR2RRbXvL8UZ96RM6WZ+S1dX2uBk9tNBDBzo8x9kCj/EIam3IGQ7gqe2R5VwqdZWRxnNxs7wdzWgGmzP6tGIhNQ1pb+KKhWzKso8rVE4BjatBZun+NBbpaHxniRKf9bvkMblr1fJfpZtbfb/dpTVev5rrT2IGxHWDuEa0a+Strnxa5CAlmDs/2aD4tXmUyC+EI9pQjutLi7PUy5hu/GPKYCcUGae027jdUe1tn08tfqI57Qt9d4632RlZyIjsXwT+KaM1GdGv/e6AvkGXFiElG+ljd5IyunHFOgm7xkwclwj5VoNZbzHZshnx13Tt3TWltSgzBukHzhbWttbJHsWCMXHNlXU3e7vZ+yDSvCdhrxJJ0ayVa8T/Ov3Vv3qdrCytCNQwzsBU2TrXfGSUs6COuuTlm22Q7mtLeaWU4aWS2vg/I9OVimTblHGhPOitB8C5T8+SF66SnOSeLvWRfrTpNBcpTxb0iKM9oixe2v2h8sAo9w3ykiu05zq0SoawCooyi9B9uVPkRb7NvKrU/WhP/y/Uja6rWkOKkTAnuFJD3Pl+TNmaLWUKq1qu3ze0m9xazxd6NfMZ01ocWXv5W2j9FfzVcutnPzq9ilW4TWtAUjBPRiOyJVrq4cfrdoWXXpmalnk2/Mya1L3slvPk19K6mRz7JJjKPq2ad+rUQtfPQ+O1ReO1pw7bdNdotKjbtSV6xeYWbXVb6csvhFs7gPKMpcxHZBqVeEhp51J+VAcsVT7H16gPLK01llYXdqt9G2DveR+ke68v7u5vS+8eibsU2/QpApP5y4B2aUIxl25tztQkBeT8ubKv9u7vUAty75EFRcryPU7cMfLWqU/lrJT0N8qzZWTnjUXQ7y2dqj7axnao/rsl5Ij2xJT2pUZ8Tj1iJb8tR7RgkVatmCOik/8uxVQy7mjOme3eZk6iSjxh8k25qwwvmSmMSf/cydvuUva6a+WvEeWEMxVd94BW+AwjBYnRJwnuyHJKM4ReTt4kyIi2R/Zz2U7JW7yxJdEqST0Xmx42Rma9Zq3ba0uPWI/tt9ATtW5m3dWD55d6c+T4nedGr0tebaRi1PnC8/lodZWXqz436WG2wNfoY0Z97MzCZHlVTEd84c1FShTGRWJ8uISNIkT+MMlDZJa3U76UdW9NuXrSIG3MMeVL3HugiHBFd9ec0dx1Zhy9JXo9wtrUZAtHCU/jMnU+YFtaPJW6uOSHZOvFRm+UWp6ozlNo6ra3MPZbWsiYrF8quDMb2duWvVPJUvhTGEmhL+QbvXX5oU3zCyj4NxKu7FBz9Dk7bEF8e0tsiTsf4W2It6ouTzQjakFbMFjIvbtqnNUezTp6a1G36ftw8OeRgK456RPypKGyS8q85DZ1f/qnZAVyEbPSm57hY7C58CNZ5hQynoQsGz+aROjv4oSORXPwGUmViz8fea/BjeJI6O80hY1BU+dHUOUQwkO/x+A356Z3OC+bU7O+lrn48pBeQN+4aBze/NXnKqafj4XKrRn5+BzQOhw1UNfe4n8dh+ZjOIXz8uU2pe+avfaYddkvVieyGA+H7xnDzWc113P055mVozPRkpufjPuioJnKrNF8fPoYj5o1oHnNhTwH5aWTeHsVGXl9qeC9gEuGTPxH/PUC/22EtyWNOjlCKOl7inpqugdPTX/j0jU6/ZmPTIZOnUxVaiaPaNEbsVtiV9yF360yAgx9O1R+l1L+R6z7+7MDaD0i66FP0eXJQYfaYjr9MLdoA3pWZ4yvLq+sL34LeblysLH6x9X1JxsrX95WX1D+VPxC/BrSknXxe/Gl2IHhHoBIfxF/E/8Q/9zc2RxvFpsnsusnFxTm56Lys/nn/wK+0PGZ</latexit> ⇢↵(x) = | det(@2'(x))|⇢ (T(x)) <latexit 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<latexit 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<latexit sha1_base64="Sgg0ElPzJvjIt54QpbUNAPlp5pE=">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</latexit> s.t. ' convex. <latexit 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<latexit 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Yann Brenier There exists a unique Monge map T. <latexit 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<latexit 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<latexit sha1_base64="nsglRAUi+tlHeI1cLZ6LHMM7xpo=">AABFXnictVxRc9y2EYbTNk3dpnHal870hY3sTNJxVUlNp53JdCa2JMuKZVv2nWQnPttD3lEn2rzj+Xg8y77oH/TX9LWd6e/oWx/bp/6FLnYBArwDuaDqmiMJBPHtLpbAYncBOpqkST7b2PjHpfe+9/0fvP/DD350+cc/+fCnH135+GfHeVZM+/FRP0uz6eMozOM0GcdHs2SWxo8n0zgcRWn8KHq5LZ8/msfTPMnG3dmbSfx0FA7HyUnSD2dQ9fzKp93TeBoH8RmwyoMwKMbJqyIO7mbjYRyMwklwtdfdvrr+/MraxvoG/gtWC5uqsCbUv8Ps40+uiJ4YiEz0RSFGIhZjMYNyKkKRw/VEbIoNMYG6p2IBdVMoJfg8FufiMmALaBVDixBqX8LvIdw9UbVjuJc0c0T3gUsKP1NABuIaYDJoN4Wy5Bbg8wIpy9o62gukKWV7A38jRWsEtTNxCrUcTrf0xcm+zMSJ+CP2IYE+TbBG9q6vqBSoFSl5YPVqBhQmUCfLA3g+hXIfkVrPAWJy7LvUbYjP/4UtZa2876u2hfg3SnkNrkB0VO+zkkIo5kg/wLdZwDOSJwXOQ6AQqz7K0mvU9Qh7P4b2C6i/B9c5lrROIrgWWHveiNyGy4XcZpF7cLmQeyzyAC4X8oBFHsLlQh4qpMROUedufAcuF77Dcn4Alwv5gEU+hMuFfMgij+FyIY9Z5LdwuZDfsshbcLmQt1jkHbhcyDsssguXC9llkUdwuZBHLHIXLhdyVyHrZ+oUrgzpJMysvAHlKg9pKVKoucHKdxOtowt702NO92uw/Kzegb9u7I6HTuMa7K7HuDupwfIjbw9spBvL26LbuJq4sLdZ7D6MADd2n8V+LV7UYL/2mGkva7D8XDuAdm4sb33vwp0be5fF3oOSG8uvUfehxo2977FiTGqwhyz2gXhVg/Wx+tMaLG/3O2BX3Fh+nepCezfWx5oWNVjenh6DB+PG8qvVI6h1Yx+x2MfirAb7mMV+A9bdjf3GY4V9W4PVa+xlXEGG6I/EMGObqIXlrJSlCVALGf5pubak6BtHUM9hhiVmiJgRi9grEXueiIMSceAtV17a0Rz9XZ5Lp0R0PBFRuTbJ0oxtPyjby1LqgdgpETtLiCaPVL5r3Zc5ehe6hkPOypVLlnz6lJX2W5ZiNR6aLa9G3K8gaGyf4si/jtGSjKCkppqonZZrPCEDvG9CvMboTfdS8+Bxs9Iq2KgzFhU5UBGLeuNAvWFRhQNVsKi5AzVnUWbm27iexwgw+pfvYoF3NALIR66/AvAKbsCqcxvmaADj5xC8wIdYcx/+djD25q4myWQ0L9dJmeV4WrHEUygtxBrUm6hwB+PrFGdYDJJRy/sqxpd3MrexUHOOrPB5uZIHZcbEn06C8gxLOtJbDHA+taNzB2vO0bujUjv87XLe61I7/C5q/By9eCq1w8+U9LMLyN5V2O4FsB2YTROlfVNuS4PyL0RDly/jqistrnyrIzVmJL2zlvT31ZvZv8B72cYS6ceU29HIrf7llf61oWH0nFt6bkdFek/k9epS0LonYxX3mnJbGTJcRcdKDnPX9s3INgP1ZnS5HY1D8Li2MeZeWOW2o3dS9saU29E4FpT3PEdPXpfb0RjiPenDlNvRkNmWUMX5ptzWsksNUOxsym2t+hizwDIHRGOeaoxXNEU/qVDUEvQPmrM1ts+/uo7JnM2zMkZopmR823o6UbmWNUuk/YUYrNqspRzSvygsH6xKYyG22PiKZJhV1vdVOmaNl5o/AC0GMPtpD4DLmacgoc5JSOudAsVNNuqq9kzjtlicHCUnS6ieqp2x3qLhS1mjat1zrOXiMtNbo8ce2uscx94EfcID1Cynh4PaN1xHkdPQQUVDPL02unur5mtV+xssbrKEmJQjrY87QrST1hynurTesXR8Te3yzOCiPR8zfmW2+URZGxnzZGiLpCxNPO12Oo9k18l19bowOW56FuAblfZqjlYjwR2pnI1CdbaYvPEF3hvaR7gnJ3kQjT68x0BRmQjaNZNZdJlPD9Ci2vaW4y31pTN0VM7R6mp73IweWuihA90+xtmGFeMelLoQMxzBXdcjyrlc6ipDjU/Fb8rd0QzfYHNEn1YspKZB9iauWMimKPu0QuU1oOVooCjdn8YyHY3vrVDio36XPCZ2rVr+a7hzq/e3Qxzj9aO5PhMzQK5byDXAWUO7unS3zIEkWDifbKH/2txLya8NR2lDOa7PLM6klzHu+McYwU7QM05xtnGzo9razk8tP9GcDoXeO5e72RlayADtXwDrU4ZjMsAf++yA3kEni5CijfSxO0np3bh8nYQdY8aPSwSdajDjLUZbViB/TdeeXTmORYoYaB04XxrbWicH6AvGyHWqrLuZ282rj0SacxL2KCGKZqx8hvw/x9/6R4+TtZURITUs30CubJ3rfWQYs0gdhbjKN9sg3daW8mopwzMltVn/jExXK5LtYMQl5ZGr9QA49/GeeMlRMkW585U2tI42ZXMl5cmSHmVvTzCKJ7s/VCuwlPs6rpJrOOd6OEqGMApmZRSh23JZ5GW+zbyq1P1o5/8X6kbXVa1JioEwGVzSEJffjzFas6VMYVTT+H2Js8mt9elSq2Y+YxyLI2sufwe1v4LfWm5970cnqliFmzgGiIK5MxqhmmClhR+vmxVeemRqWube8DNjUreyay4SX5N1MzH2vDWVQxw1ZyprocsXofHCovHCU4dd3Gs0WtT12hI9Z2OLrtqt9OXXhlu3BeWCpcx7ZBqVeEhpx1J+VAcsVT7G16i3LK0NllYIs9XeDbDnvA/SPdeXZ/d35eoeiFvo2/TRA6P4ZYCzNEGfS9c2R2pEQXL+QtlXe/b3sEZyj9CCSsp0jlPOGNp16uN1Xkr6qVrZMrTzxiLoc0uvVRttY3tY/t0KcoRzIsd5qRFfYItYyW/LESxZpHXL5wgw8x+iT0V+R3PMbLc27ySo+BMm3qRZZXhRpDBG/XOZt/2V6HXfil8DjAkL5V1HQKv9G5YUCKMzCW7PMsc3JFc52kkgjzZC+7lqp2gXb2xJtI5SL8SfPGwMRb1mrNtjS/dY9+3X0FJq3bx1VwueX+rNkeN3kR29EFe1kfJRF0v3F6MVqlWuet+kh2KJr9FHgW3syMJEeVVMT3zpzYUkaseFMD5c2vWijfztJG8jM+1O+VLWrTXlaqaBbMwpxkvcOVCJcHl3nzm9uc+ZfkQr9CLE2tSohqMks3GZyg/YllZmpYKlCMmu59ak1FqP6tYLw8NeNYwdJ0sZoxVMBZe7odZ2H3qVaIXPxhCFvqCTvXVxok3zS7jk70C4okTN0SeH2AE/94bYFrvv4FTEK1WmzGaANdImDJZi8FD1s9qiWUevLOo2fR8O/jwS0DUnfYIralvZiTIvuU3dn/5rtAZTEbPSm5bt+2Bz4XuyyqlNfxK0cHxvEqG/yWnbF83BpydVLv58aH+D68WJ0N82teuDps73oMqhDQ99nsHvnZvW7XnZnJr1tcrFlwetA3rnRePkDmB9zGLa+VioqfVG3j0HaR1OGqjr1eJ/7YfmYzi15+XLLcdvzl54vHVqF6vMrPSL288Zw81nNNdz9OeZlb0zXpObH/l/Qas3lVm9eff0pV9qxoDmtRCUD+WlI7w9ioy8vlTk/oBLhkz8R/z9Ev9VwquSRp0cbSjp/Yp6aroFT01/eenqnX7mI5OhUydTlZqJJzp4MnZb7Itb8LNdeoBtT4nSN5X0V2Ld39EOoPYErYfOplMGoYd1MWZBzG7aAO/NOdo6ieWZXjrj24UauSd+gLXyvO89bC/P/HYrfav/koTm+l2RiUElMlne5TPzKoIeVHfgKBekv/cN8Ew9ZbPoBNrIY4+RzlFRpKS/fl4gYoBx4bKkC0To0dJEOXJSjvBMUlxDO6r0rY8jfKJ2+uW+gzyfH5bZpUD8FutCtTrIlbpJ64fqO+CqTE8wLxCh9jcgPvu9uA5/r6uyW85Dweeguhfi1l3qf45vttrPM+tZ8/myc+doM99IXsPsms7/zVW7DHMFZk+yOb+7U8uFztE344cN+KElZQfHwEuM5qeiOSNZNNAslEz2LvFY6Gwq6UHGyGE56pqj8nkDr7lH/+/Uou9Yku6BLBHm8APcJZwivVTpZhelp9Oazdng2w3S6m9BiaY5r2nGgT552bzTkDrHvW1T6HQllwGKa+jYFoTOeXJnUJILzvuJxxmL0KO3fF99espRKVhJCo/vm+cessw96Jww0pywFIasJMo+PL+ytrn8P4isFo631jc31jcfbK19dVP97yIfiF+KT8RnsKL+QXwF4/9QHAGnP4u/iL+Kv+38c/f93Q93P6Km711SmJ+Lyr/dX/wX0NJaBg==</latexit> It is the unique T = r' such that <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="jRX8giyUu12rfn1251pXgPCW+54=">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</latexit> ' is convex and (r')]↵ = . <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="tvjr0hwMzBZ6qILEwzAGLTMLlqQ=">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</latexit> Theorem: [Brenier, 1991] <latexit 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<latexit 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↵ <latexit 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<latexit 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W2 2 (↵, ) def. = inf =T ]↵ Z Rd ||x T(x)||2d↵(x) <latexit 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<latexit 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<latexit 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<latexit 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X = Rd <latexit 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<latexit 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  30. Regularity Theory Alessio Figalli ! Regularity of T requires convex

    target. <latexit 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<latexit 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<latexit 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  31. Regularity Theory Alessio Figalli ! Regularity of T requires convex

    target. <latexit 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<latexit 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<latexit 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  32. <latexit sha1_base64="lkYmEXSwz6mt4AGHn22Q31ywqqo=">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</latexit> C↵(x) def. = R x 1 d↵ <latexit

    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<latexit 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<latexit 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<latexit 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↵ <latexit 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1-D Optimal Transport C↵] : ↵ 7 ! U[0,1] <latexit 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<latexit 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<latexit 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<latexit 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Cumulative function: <latexit 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<latexit 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<latexit 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<latexit 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  33. <latexit sha1_base64="lkYmEXSwz6mt4AGHn22Q31ywqqo=">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</latexit> C↵(x) def. = R x 1 d↵ <latexit

    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<latexit 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<latexit 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<latexit 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↵ <latexit 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1-D Optimal Transport C↵] : ↵ 7 ! U[0,1] <latexit 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<latexit 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<latexit 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<latexit 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Cumulative function: <latexit 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<latexit 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<latexit 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<latexit 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  34. <latexit sha1_base64="lkYmEXSwz6mt4AGHn22Q31ywqqo=">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</latexit> C↵(x) def. = R x 1 d↵ <latexit

    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<latexit 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<latexit 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<latexit 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↵ <latexit 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<latexit 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C 1 ↵ <latexit 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  35. <latexit sha1_base64="lkYmEXSwz6mt4AGHn22Q31ywqqo=">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</latexit> C↵(x) def. = R x 1 d↵ <latexit

    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<latexit 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<latexit 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<latexit 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↵ <latexit 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Optimal transport ↵ 7! : <latexit 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<latexit 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<latexit 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T = C 1 C↵ <latexit 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<latexit 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1-D Optimal Transport C 1 ] : U[0,1] 7 ! <latexit 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<latexit 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<latexit 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Quantile function: <latexit 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<latexit 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C↵] : ↵ 7 ! U[0,1] <latexit 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<latexit 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<latexit 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<latexit 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Cumulative function: <latexit 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<latexit 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<latexit 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<latexit 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C 1 ↵ <latexit 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  36. <latexit 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↵ <latexit 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<latexit

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<latexit 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<latexit sha1_base64="cOXoTQGOwUSDpobZ06nn8bk1NgM=">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</latexit> C↵(x) def. = R x 1 d↵ <latexit 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<latexit 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<latexit 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<latexit sha1_base64="NagChymWaASb8bvGA6rN+HpPF8Q=">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</latexit> W1(↵, ) = ||↵ ||W1 = R R |C↵(x) C (x)|dx <latexit 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<latexit 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<latexit 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<latexit sha1_base64="LTA4z6RcvQ5fpn9AKnIpN2fJHaE=">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</latexit> Wp(↵, )p def. = R ||T(x) x||pd↵(x) = R 1 0 |C 1 ↵ (t) C 1(t)|pdt <latexit 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<latexit 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<latexit 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<latexit 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  37. <latexit 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↵ <latexit 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<latexit

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<latexit 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<latexit sha1_base64="cOXoTQGOwUSDpobZ06nn8bk1NgM=">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</latexit> C↵(x) def. = R x 1 d↵ <latexit 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<latexit 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<latexit 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<latexit sha1_base64="NagChymWaASb8bvGA6rN+HpPF8Q=">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</latexit> W1(↵, ) = ||↵ ||W1 = R R |C↵(x) C (x)|dx <latexit 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<latexit 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<latexit 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<latexit sha1_base64="LTA4z6RcvQ5fpn9AKnIpN2fJHaE=">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</latexit> Wp(↵, )p def. = R ||T(x) x||pd↵(x) = R 1 0 |C 1 ↵ (t) C 1(t)|pdt <latexit 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<latexit 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<latexit 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<latexit 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  38. <latexit 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↵ <latexit 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<latexit

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<latexit 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<latexit sha1_base64="cOXoTQGOwUSDpobZ06nn8bk1NgM=">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</latexit> C↵(x) def. = R x 1 d↵ <latexit 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<latexit 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<latexit 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<latexit sha1_base64="NagChymWaASb8bvGA6rN+HpPF8Q=">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</latexit> W1(↵, ) = ||↵ ||W1 = R R |C↵(x) C (x)|dx <latexit 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<latexit 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<latexit 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<latexit 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||↵ ||2 K = R 1 0 |C↵(t) C (t)|2dt <latexit 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AUC(↵, ) = 1 R 1 0 C↵ C 1(x) <latexit 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<latexit 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<latexit 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||↵ ||KS = supx |C↵(x) C (x)| <latexit 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<latexit 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<latexit 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Wp(↵, )p def. = R ||T(x) x||pd↵(x) = R 1 0 |C 1 ↵ (t) C 1(t)|pdt <latexit 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<latexit 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<latexit 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  39. <latexit sha1_base64="lkYmEXSwz6mt4AGHn22Q31ywqqo=">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</latexit> C↵(x) def. = R x 1 d↵ <latexit

    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<latexit 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<latexit 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Optimal transport interpolation ↵0 $ ↵1 <latexit 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1-D Optimal Transport Interpolation C↵0 <latexit 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8 t 2 [0, 1], C 1 ↵t = (1 t)C 1 ↵0 + tC 1 ↵1 <latexit 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<latexit 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<latexit 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<latexit 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  40. <latexit sha1_base64="lkYmEXSwz6mt4AGHn22Q31ywqqo=">AABB1nictVzbchu5EYU3l107N2+St7xMonXKm3IcSdmqpLKVqpUlWdaatmWTkr27tF28jGjaQw7NIekLV3lL5TWfkNfkJ/Id+YPkKb+QvgADDImZxiheoyRhQJzuRg/Q6G6A7k6SYTbb3PzXhfe+9e3vfPf9Dy5e+t73f/DDH13+8McnWTqf9uLjXpqk00fdThYnw3F8PBvOkvjRZBp3Rt0kfth9sYufP1zE02yYjluzN5P48agzGA9Ph73ODJqeXv7p7nw0T+BhEUen83EPW//w9PLG5vVN+hetV7Z0ZUPpf0fph9Gxaqu+SlVPzdVIxWqsZlBPVEdlUL5SW2pTTaDtsVpC2xRqQ/o8VmfqEmDn0CuGHh1ofQG/B/D0lW4dwzPSzAjdAy4J/EwBGakrgEmh3xTqyC2iz+dEGVvLaC+JJsr2Bv52Na0RtM7UM2iVcKZnKA7HMlOn6vc0hiGMaUItOLqepjInraDkkTOqGVCYQBvW+/D5FOo9Qho9R4TJaOyo2w59/m/qia343NN95+o/JOUVKJFq6tGnOYWOWhD9iN7mHD5jeRLgPAAKsR4j1l6Rrkc0+jH0X0L7XShnVDM66UJZUutZJXIXig+5KyIPoPiQByKyAcWHbIjIIyg+5JFGInZKOvfjm1B8+KbI+T4UH/K+iHwAxYd8ICJPoPiQJyLySyg+5Jci8iYUH/KmiLwNxYe8LSJbUHzIlog8huJDHovIfSg+5L5Glq/UKZSU6AyFVbkD9SIPtBQJtOyI8t0g6+jD3ghY070SrLyq9+CvH7sXoNO4BLsfMO9OS7DyzDsAG+nHyrboFu0mPuwtEXsIM8CPPRSxn6vnJdjPA1baixKsvNYa0M+Pla3vHXjyY++I2LtQ82PlPeoetPix9wJ2jEkJ9kjE3lcvS7AhVn9agpXtfhPsih8r71Mt6O/HhljTeQlWtqcn4MH4sfJu9RBa/diHIvaRel2CfSRivwDr7sd+EbDDvi3Bmj32Eu0gA/JHYlixVdQ6+arE2gSodQT+Sb63JOQbd6FdwgxyzIAwIxFxkCMOAhGNHNEIlivL7WhG/q7MpZkjmoGIbr43YW0m9u/n/bGWBCD2csTeCqLKI8V3bcayIO/CtEjIWb5zYS1kTGluv7EW6/lQbXkN4l4BwXP7Gc38axQtYQSFmqqi9izf4xkZ0XMV4hVFb2aUhoeMm+VWwUW9FlFdD6orot54UG9E1NyDmouohQe1EFF25bu4dsAMsPrHd7GkJ54B7COXlwi8gh3YdW7BGo1g/hyBF/iAWu7B3ybF3lKpkgyjedwnMcvxuGCJp1Bbqg1ot1HhHsXXCa2wGCTjnvd0jI9PmNtY6jXHVvgs38mjPGMSTmdI8gxyOugtRrSe6tG5TS1n5N1xrR7+Vr7uTa0efp80fkZePNfq4Wda+tk5ZG9pbOsc2CasponWvq3XpcH5F6Zh6pdo10WLi291pOcM0ntdk/6hfjOH53gvu1Rj/dh6PRqZM76sML46NKyeM0fP9aig98Rer6lFtUcy1nGvrdeVIaVddKzlsE913wz26es3Y+r1aByBx7VLMffSqdedvZN8NLZej8aJ4rznGXnypl6PxoCeWR+2Xo8GZls6Os639bqWHTXAsbOt17XqY8oCYw6I5zy3WK9oSn7SXFMbkn9Qna1xff71fQxzNk/yGKGakvVty+l0872sWiLjL8Rg1WY15UD/Yu74YEUaS7Utxlcsw6ywv6/TsXs8ar4BWoxg9fMZgJQzT0BCk5NA650AxS0x6iqOzOC2RRzOktMVVFu3zkRv0fLlrFGx7Sm1SnGZHa3VY5vsdUZzb0I+YYM0K+mhUfqGyyhKGmoUNCTTq6O7t3q9FrW/KeImK4hJPtN6dCLEJ2nVcapP601Hx1f0Kc8MCp/52PmL2eZTbW0w5knJFqEsVTzdfiaP5LbhvnpN2Rw3fxbRG0V7tSCrMaQTqUyMQk22mL3xJT1b2sd0Joc8mEYP3mOkqUwUn5phFh3z6RFZVNfeSrxRXyZDx/WMrK6xx9XogYMeeND1Y5xd2DHuQq0FMcMxPLUCopxLua5S0vhU/To/HU3pDVZH9EnBQhoabG/igoWsirKfFai8AjTOBo7Sw2ms0jH49holOer3yWNj16Llv0Int+Z8u0NzvHw2l2di+sR1m7hGtGr4VJefVjmwBEvvJ9vkv1aPEvnV4Yg2VOL6xOHMehnTiX9MEeyEPOOEVpu0Ooq93fzU6ieG05EyZ+d4mp2ShYzI/kWwP6U0JyP6ce8OmBN0tggJ2cgQuzPMvRufrzMU55j144aKbzXY+RaTLZsTf0PXXV0ZzUWOGHgfOFuZ20YnDfIFY+I61dbdru3q3QeR9p6EO0uYop0rV4n/x/Tb/Jh5srE2I1DD+AYybet87yOlmAV11KFdvtoGmb6ulB/lMjzRUtv9z8r0UUGyPYq4UB7crfvAuUfPzAtnyZTkztb68D5alc1FypMVPeJoTymKZ7s/0Dswyn2NdskNWnNtmiUDmAWzPIowfaUs8irfal5F6mG0s2+EutV1UWtIMVI2g8sakvL7MUVrrpQJzGqevy9oNfm1Pl3pVc1nTHNx5Kzlr6H15/DbyG2ew+h0C1bhBs0BpmCfrEa4JVrrEcbrRoGXmZmGln22/OycNL3clvPE12zdbIy9qE3liGbNa521MPXz0Hju0HgeqMMWnTVaLZp2Y4meirFFS59WhvKrw61Vg/JcpCx7ZAY1DJDSjaXCqPZFqnKMb1BvRVqbIq0OrFb3NMBd8yFI/1pfXd1f57t7pG6Sb9MjD4zjlz6t0iH5XKa1OlJjCsj5E21f3dXfphbk3iULipT5HieuGD516lE5yyX9pd7ZUrLz1iKYe0uvdB9jY9tU/+0ackRrIqN1aRCfUI9Yy+/KEa1YpOuOzxFR5r9DPhX7HdUxs9vbvpOo4E/YeJNXleXFkcKY9C9l3g7XotdDJ36NKCaca++6C7Tqv2GkwBiTSfB7lhm9Idzl+CSBPdou2c91O8WneGNHousk9VL9McDGcNRr57o7t8yIzdh+BT1R6/at+3rI/JJgjhK/85zodWhXG2kfdbnyfD5aHb3LFZ+r9DBf4Wv1Mac+bmRho7wipq0+DebCEtXjwpgQLvVGUUf+epLXkZlPp0Ipm96GcjHTwDbmGcVL0j1QRPi8u6teb+5jYRzdNXpdwrrUuEWihNm4VOcHXEuLWamLa/sQt16s3I0SZycq2ykMdXe3sPabLWRM1i9RUs6Ge7uytwtRipyFYQo9xTd6y+JDl+anUPB3pHzRoeEYkjtsgn+7o3bV/ju4DfFS1zmjGVEL2oL+Suzd0eMs9qjW0UuHuks/hEM4jyHoWpJ+SDtpXdmZsiy5Sz2c/iuyAlMVi9LbnvXH4HKRR7LOqc54hmTZ5NEMlfkuTt2xGA4hIylyCefD5xrSKE6V+U5TvTEY6vIIihzq8DD3GMLeue1dn5fLqVpf61xCefAuYE5cDA5P/spjFdsvxEJNnTfy7jmgdTitoG52i/93HIaP5VSfVyi3jL5r9jzgrXO/WGdk0R+uv2Yst5DZXM4xnGeaj856S35+7PdFtd5U6ozm3dNHf9TOAcNrqTgPKkvHeHcWWXlDqeC5gE+GVP1X/fOC/G2ElzmNMjnqUDLnFOXUTA+ZmvnGpW905rMQmSydMpmK1Gwc0aQbsbvqUN2En93cA6x7O5S/S8l/Eev//mwfWk/JepgsOmcO2tQWU/bDnqL16dneny2TGO/y8t3eFrTgWXiDWvGe713qj3d9W4WxlX+DhNf6HZWqfiEiWT3ds+uqCyMonrxxDsh8zzeiu/ScxeKbZ6OAs0Vzf2pVoiV9It8s6Jbiu46UPZqrE31WjycHeMO+k+eHIvUbautoO497rsT5qJTz0QrnjLRT5PDa+az6blYZl12HSz/PnS10v5TibHueV50b3SvlwnfQq/GDCvzAkbJJ2n9BkfBUVWfz5hU051om94R1rEwmkvWAcWYnf9/Vke2igtciYPy3S9G3HUkPQJYu5b8jOmGbEr1E62afpOebjtWZ1FsV0urvUT69vLG1+n8ZrFdOtq9vbV7fur+98dkN/f8cfKB+pn6hrsIa/536DKgdqWPg8Fb9Tf1d/WPn0c6fdv688xfu+t4FjfmJKvzb+ev/AMEHqPA=</latexit> C↵(x) def. = R x 1 d↵ <latexit

    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<latexit 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<latexit 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Optimal transport interpolation ↵0 $ ↵1 <latexit 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1-D Optimal Transport Interpolation C↵0 <latexit 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8 t 2 [0, 1], C 1 ↵t = (1 t)C 1 ↵0 + tC 1 ↵1 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  41. OT Between 1D Gaussians d↵ dx = 1 ↵ p

    2⇡ e (x m↵)2 2 2 ↵ <latexit 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<latexit 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<latexit 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T(x) = ↵ (x m↵) + m <latexit 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<latexit 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  42. OT Between 1D Gaussians d↵ dx = 1 ↵ p

    2⇡ e (x m↵)2 2 2 ↵ <latexit 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<latexit 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<latexit 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T(x) = ↵ (x m↵) + m <latexit 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<latexit 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<latexit sha1_base64="z1Y1ThFmiS5ElUvQSw4BfapzddM=">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</latexit> ' is convex. <latexit 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<latexit 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T ⌘ OT <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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=) <latexit 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<latexit 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Brenier <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="aF0eXQkPIn/NhvUyA6v9n+hBmsI=">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</latexit> '(x) = 2 ↵ (x m↵)2 + m x <latexit 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<latexit 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<latexit 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  43. OT Between 1D Gaussians d↵ dx = 1 ↵ p

    2⇡ e (x m↵)2 2 2 ↵ <latexit 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<latexit 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<latexit 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T(x) = ↵ (x m↵) + m <latexit 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<latexit 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W2 2 (↵, ) = (m↵ m )2 + ( ↵ )2 <latexit 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<latexit 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<latexit 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T = r' <latexit 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<latexit 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<latexit sha1_base64="z1Y1ThFmiS5ElUvQSw4BfapzddM=">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</latexit> ' is convex. <latexit 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<latexit 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T ⌘ OT <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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=) <latexit 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<latexit 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Brenier <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="aF0eXQkPIn/NhvUyA6v9n+hBmsI=">AABFyXictVzbchu5EYU3t41z8yaPeZms1ilvynEkZVNJ1Vaq1rpY0kpryyYle9eyXRxyRFMecejhxbK5esoX5DX5mHxH/iB5yi+kL8AAQ2KmMYrjKUkYEKe70QAa3Q3Q8SgdjCerq/+89sF3vvu97//gwx9e/9GPf/LTn9346OfH42yad5OjbpZm+ZO4M07SwTA5mgwmafJklCed8zhNHsevNvHzx7MkHw+yYXvydpQ8O+/0h4PTQbczgarHG3kyHCT5ixsrq3dW6V+0XFjThRWl/x1mH318rE5UT2Wqq6bqXCVqqCZQTlVHjeF5qtbUqhpB3TM1h7ocSgP6PFGX6jpgp9AqgRYdqH0Fv/vw9lTXDuEdaY4J3QUuKfzkgIzUTcBk0C6HMnKL6PMpUcbaKtpzoomyvYW/saZ1DrUT9RJqJZxpGYrDvkzUqfoT9WEAfRpRDfauq6lMSSsoeeT0agIURlCH5R58nkO5S0ij54gwY+o76rZDn/+LWmItvnd126n6N0l5E55ItXTvs4JCR82IfkSjOYXPWJ4UOPeBQqL7iKU3pOtz6v0Q2s+h/j48l1QyOonhmVPtZS1yEx4fclNE7sDjQ+6IyAN4fMgDEXkIjw95qJGIzUnnfnwLHh++JXJ+CI8P+VBEPoLHh3wkIo/h8SGPReQ38PiQ34jIe/D4kPdE5D48PuS+iGzD40O2ReQRPD7kkYjchseH3NbI6pWaw5MRnYGwKu9CucwDLUUKNXdF+TbIOvqwGwFruluBlVf1Fvz1Y7cCdJpUYLcD5t1pBVaeeTtgI/1Y2Rbt0m7iw+6K2D2YAX7snoj9Up1VYL8MWGmvKrDyWjuAdn6sbH2/gjc/9isRex9Kfqy8Rz2AGj/2QcCOMarAHorYh+p1BTbE6ucVWNnut8Cu+LHyPtWG9n5siDWdVmBle3oMHowfK+9Wj6HWj30sYp+oiwrsExH7NVh3P/brgB32XQXW7LHXaQfpkz+SwIqto9YpViWWRkCtI/BPi70lJd84hnoJ0y8wfcKci4idArETiDgoEAfBco0LOzomf1fm0ioQrUBEXOxNWJqI7XtFeyylAYitArG1gKjzSHGsTV9m5F2YGgk5KXYuLIX0KSvsN5YSPR/qLa9BPCgheG6/pJl/m6IljKBQU3XUXhZ7PCMjeq9DvKHozfTS8JBxk8IquKgLERV7ULGIeutBvRVRUw9qKqJmHtRMRNmV7+JOAmaA1T+OxZzeeAawj1z9ROAV3IVdZxfWaATz5xC8wEdU8wD+tij2lp46yTCax30SsxzPSpY4h9JcrUC9jQq3KL5OaYUlIBm3fKBjfHzD3MZcrzm2wpfFTh4VGZNwOgOSp1/QQW8xovXUjM4+1VySd8elZvjdYt2bUjP8Nmn8krx4LjXDT7T0kyvI3tbY9hWwLVhNI619W25Kg/MvTMOUr9OuixYXR/Vczxmkd9GQ/p4emb0rjMsmlVg/ttyMxtjp37jUvyY0rJ7Hjp6bUUHvib1eU4oa92So415bbipDRrvoUMth35qODLbp6ZEx5WY0DsHj2qSYe+6Um87eUdEbW25G41hx3vOSPHlTbkajT++sD1tuRgOzLR0d59tyU8uOGuDY2ZabWvUhZYExB8RznmusV5STnzTV1AbkH9Rna1yff3kfw5zN8yJGqKdkfdtqOnGxl9VLZPyFBKzapKEc6F9MHR+sTGOu1sX4imWYlPb3ZTp2j0fNH4AWI1j9fAYg5cxTkNDkJNB6p0BxTYy6yj0zuHURh7PkdAF1omsnordo+XLWqFz3gmqluMz21urxhOz1mObeiHzCA9KspIeDyhGuoihp6KCkIZleE9290+u1rP1VETdaQIyKmdalEyE+SauPU31abzk6vqlPeSbw8JmPnb+YbT7V1gZjnoxsEcpSx9NtZ/JIbh3uq7eVzXHzZxGNKNqrGVmNAZ1IjcUo1GSL2Ruf07ulfURncsiDaXRhHCNNZaT41Ayz6JhPj8iiuvZW4o36Mhk6Lo/J6hp7XI/uO+i+B908xtmEHeM+lNoQMxzBWzsgyrle6Cojjefqt8XpaEYjWB/RpyULaWiwvUlKFrIuyn5ZovIG0DgbOEoPp7FIx+BPlijJUb9PHhu7li3/TTq5NefbHZrj1bO5OhPTI67rxDWiVcOnuvy2yIElmHs/WSf/tb6XyK8JR7ShEtfnDmfWy5BO/BOKYEfkGae02qTVUW7t5qcWPzGcDpU5O8fT7IwsZET2L4L9KaM5GdGPe3fAnKCzRUjJRobYnUHh3fh8nYE4x6wfN1B8q8HOt4Rs2ZT4G7ru6hrTXOSIgfeBy4W5bXRyQL5gQlxzbd3t2q7ffRBp70m4s4Qp2rlyi/h/Sr/Nj5knK0szAjWMIzDWts43HhnFLKijDu3y9TbItHWl/KSQ4bmW2u5/VqZPSpJtUcSF8uBu3QPOXXpnXjhLcpJ7vNSG99G6bC5SHi3oEXt7SlE82/2+3oFR7tu0S67QmjuhWdKHWTApogjTVsoiL/Kt51WmHkZ7/H+hbnVd1hpSjJTN4LKGpPx+QtGaK2UKs5rn7ytaTX6t5wut6vkMaS6eO2v5W6j9Ffw2cpv3MDpxySps0BxgCvbNaoRroqUWYbw2SrzMzDS07LvlZ+ekaeXWXCW+ZutmY+xZYyqHNGsudNbClK9C48yhcRaowzadNVotmnpjiV6IsUVbn1aG8mvCrd2A8lSkLHtkBjUIkNKNpcKo9kSqcoxvUO9EWqsirQ6sVvc0wF3zIUj/Wl9c3d8Wu3uk7pFv0yUPjOOXHq3SAflcprY+UmMKyPkzbV/d1X9CNcg9JguKlPkeJ64YPnXq0nNZSPprvbNlZOetRTD3lt7oNsbGnlD590vIc1oTY1qXBvEZtUi0/K4c0YJFuuP4HBFl/jvkU7HfUR8zu63tmEQlf8LGm7yqLC+OFIakfynztrcUve458WtEMeFUe9cx0Go+wkiBMSaT4PcsxzRCuMvxSQJ7tDHZz2U7xad4Q0eiOyT1XP05wMZw1Gvnuju3TI9N334DLVHrdtR9LWR+aTBHid9VTvQ6tKudax91vvB+NVodvcuV3+v0MF3ga/UxpTZuZGGjvDLmRH0ezIUlasaFMSFcmvWiifzNJG8iM59OhVI2rQ3lcqaBbcxLipeke6CI8Hl3t7ze3KdCP+IlejFhXWpcI1HCbFym8wOupcWsVLQQIbn10p6UOvtR1X5hebi7hrXjbCkTsoKpknI33Nrtw0kpWpGzMUyhq/hmb1Wc6NL8HB78HSlflGg4huQQW+Dn3lWbavs93Ip4rcuc2YyoBm1CbyEG7+h+llvU6+i1Q92lH8IhnMcAdC1JP6AdtansTFmW3KUeTv8NWYNcJaL0tmXzPrhc5J4sc2rSnwFZOLk3A2W+k9O0L4ZDSE/KXML58PmG1ItTZb7b1KwPhrrcgzKHJjzMfYawMbetm/NyOdXra5lLKA/eB8zJi8HhCWB1zGLbhVio3BmR988BrcNpDXWzW/yv/TB8LKfmvEK5jek7Z2cBo87tEp2ZRb+4+Zqx3EJmczXHcJ5Z0TvrNfn5sf8XNRqpzOnN+6ePfqmdA4bXXHE+VJaO8e4ssvKGUsHzAZ8MmfqP+sc1+VsJrwsaVXI0oWTOK6qpmRYyNfPNS1/vzGchMlk6VTKVqdl4okU3YzfVnroHP5uFB9j0lih/p5L/Itb/Pdoe1J6S9TDZdM4gnFBdQlkQe5rWo3d7j7ZKYrzTy3d821CDZ+IHVIv3fe9Te7zz2y71rfqbJLzWv1KZ6pUik8VTPruuYuhB+QSOc0Hm+74R3annbBbfQDsPOGPke1QcKZlvP88J0aO4cFHSOSHMbKmjHHspx3QnKamgHZf61qUZPtIn/XjugPfzO0V2KVK/o7qO3h1wp67T+qH+HnBZpqeUF4hJ+6sQn/1B3Ya/t3XZL+ehknNQ7Stxayub/ak+1/VRtqMmnwyfVVCwo3Om3DXMYzGmWVbW+YXzWf1dt0vvzLff17xJmT6Ti5zpdhnlLez5aH2ueauSC9/pr8f3a/B9R8oWzcdXlFnIVX12dFpDc6plck+sh8pkdlkPGK93ihVQnyGY1fCaBfR/vxK970i6A7LEdJ4Q0YllTvRSrZttkp5vjtZnpndrpN1V1hpHyt4dtfPA3AKtP/VIhZVibnpK2ahEXC/mzql0H8a/dmUbNApY1Z2A3sp9DempRGUqSjIN+K71LECWWQCdU0GaU5FCX5RE24cXN1bWFv83k+XC8fqdtdU7aw/XV77Y0P/TyYfql+pjdQt29z+qL2D+H6oj8mn+qv6m/r69v/16+2L7HTf94JrG/EKV/m3/5b+WYmw1</latexit> '(x) = 2 ↵ (x m↵)2 + m x <latexit 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<latexit 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<latexit 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  44. OT Between 1D Gaussians d↵ dx = 1 ↵ p

    2⇡ e (x m↵)2 2 2 ↵ <latexit 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<latexit 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<latexit 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T(x) = ↵ (x m↵) + m <latexit 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<latexit 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m W2 2 (↵, ) = (m↵ m )2 + ( ↵ )2 <latexit 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<latexit 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<latexit 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T = r' <latexit 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<latexit 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<latexit sha1_base64="z1Y1ThFmiS5ElUvQSw4BfapzddM=">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</latexit> ' is convex. <latexit 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<latexit 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T ⌘ OT <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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=) <latexit 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<latexit 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Brenier <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="aF0eXQkPIn/NhvUyA6v9n+hBmsI=">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</latexit> '(x) = 2 ↵ (x m↵)2 + m x <latexit 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<latexit 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<latexit 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  45. OT Between Gaussians d↵ dx = 1 (2⇡)d/2|⌃↵ | e

    | |x m↵| |2 ⌃ 1 ↵ 2 <latexit 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<latexit sha1_base64="3B7Qx0kpEh+2zJ3dVel5SSzFJHk=">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</latexit> ⌃↵ = U↵ diag( ↵)U> ↵ <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  46. OT Between Gaussians d↵ dx = 1 (2⇡)d/2|⌃↵ | e

    | |x m↵| |2 ⌃ 1 ↵ 2 <latexit 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<latexit sha1_base64="3B7Qx0kpEh+2zJ3dVel5SSzFJHk=">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</latexit> ⌃↵ = U↵ diag( ↵)U> ↵ <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="NeaxpuVMi5Zi+lTnfVYO2Lny/kc=">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</latexit> Proposition: <latexit 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<latexit 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<latexit 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T(x) = A(x m↵) + m <latexit 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<latexit 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  47. OT Between Gaussians: Bures Distance A = ⌃ 1 2

    ↵ q ⌃ 1 2 ↵ ⌃ ⌃ 1 2 ↵ ⌃ 1 2 ↵ <latexit 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<latexit 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<latexit 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<latexit 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Bures distance: <latexit 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<latexit 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<latexit 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B(⌃↵, ⌃ )2 def. = tr ⇣ ⌃↵ + ⌃ 2 q ⌃ 1 2 ↵ ⌃ ⌃ 1 2 ↵ ⌘ <latexit 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<latexit 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W2 2 (↵, ) = ||m↵ m ||2 + B(⌃↵, ⌃ )2 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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T(x) = A(x m↵) + m <latexit 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<latexit 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  48. OT Between Gaussians: Bures Distance A = ⌃ 1 2

    ↵ q ⌃ 1 2 ↵ ⌃ ⌃ 1 2 ↵ ⌃ 1 2 ↵ <latexit 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<latexit 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<latexit 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<latexit sha1_base64="3H61pzHjb76TAvsW3bvwpEDc1RM=">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</latexit> If ⌃↵⌃ = ⌃ ⌃↵: <latexit 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<latexit 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B(⌃↵, ⌃ )2 = || p ⌃↵ p ⌃ ||2 <latexit 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<latexit 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Bures distance: <latexit 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<latexit 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<latexit 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B(⌃↵, ⌃ )2 def. = tr ⇣ ⌃↵ + ⌃ 2 q ⌃ 1 2 ↵ ⌃ ⌃ 1 2 ↵ ⌘ <latexit 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<latexit 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W2 2 (↵, ) = ||m↵ m ||2 + B(⌃↵, ⌃ )2 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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T(x) = A(x m↵) + m <latexit 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<latexit 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  49. Interpolation Between Gaussians Optimal transport map T]↵ = . <latexit

    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<latexit 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<latexit 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m↵ <latexit 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<latexit 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<latexit 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<latexit 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T(x) = A(x m↵) + m <latexit 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<latexit 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A = ⌃ 1 2 ↵ ⇣ ⌃ 1 2 ↵ ⌃ ⌃ 1 2 ↵ ⌘1 2 ⌃ 1 2 ↵ <latexit 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<latexit 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Displacement interpolation: <latexit 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<latexit 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<latexit 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↵t def. = ((1 t)Id + tT)]↵ = N(mt, ⌃t) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="VslKX6mw8qcHzc5IyfZVjIIOdHw=">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</latexit> mt = (1 t)m↵ + tm <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="zqI5LzxQ2JgKcVxHiDXih/N9wK8=">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</latexit> ⌃t = [(1 t)Id + tA]⌃↵[(1 t)Id + tA] <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  50. Interpolation Between Gaussians Optimal transport map T]↵ = . <latexit

    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<latexit 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<latexit 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m↵ <latexit 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<latexit 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<latexit 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<latexit 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T(x) = A(x m↵) + m <latexit 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<latexit 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A = ⌃ 1 2 ↵ ⇣ ⌃ 1 2 ↵ ⌃ ⌃ 1 2 ↵ ⌘1 2 ⌃ 1 2 ↵ <latexit 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<latexit 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Displacement interpolation: <latexit 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<latexit 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<latexit 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↵t def. = ((1 t)Id + tT)]↵ = N(mt, ⌃t) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="VslKX6mw8qcHzc5IyfZVjIIOdHw=">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</latexit> mt = (1 t)m↵ + tm <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="zqI5LzxQ2JgKcVxHiDXih/N9wK8=">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</latexit> ⌃t = [(1 t)Id + tA]⌃↵[(1 t)Id + tA] <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  51. Kantorovitch’s Formulation ↵ = Pn i=1 ai xi = Pm

    j=1 bj yj Points (xi)i, (yj)j Weights ai > 0, bj > 0. Pn i=1 ai = Pm j=1 bj = 1 xi <latexit 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sha1_base64="lHCrrCdLriSUoJxIcVw6BefNKNo=">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</latexit> Discrete distributions: <latexit 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<latexit 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<latexit 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<latexit sha1_base64="mdlENPIKtv1PnSOEu/s/cH99nYI=">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</latexit>
  52. Kantorovitch’s Formulation ↵ = Pn i=1 ai xi = Pm

    j=1 bj yj Points (xi)i, (yj)j Weights ai > 0, bj > 0. Pn i=1 ai = Pm j=1 bj = 1 b <latexit sha1_base64="LhlbHqBkrxCDCHirUc/UdkhSooo=">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</latexit> <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Couplings: <latexit 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<latexit 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<latexit 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P j Pi,j = ai <latexit 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<latexit 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<latexit 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<latexit 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P i Pi,j = bj <latexit 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P > 0, P1m = a, P>1n = b <latexit 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<latexit 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<latexit 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sha1_base64="lHCrrCdLriSUoJxIcVw6BefNKNo=">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</latexit> Discrete distributions: <latexit 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<latexit 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<latexit 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<latexit sha1_base64="mdlENPIKtv1PnSOEu/s/cH99nYI=">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</latexit>
  53. Kantorovitch’s Formulation ↵ = Pn i=1 ai xi = Pm

    j=1 bj yj Points (xi)i, (yj)j Weights ai > 0, bj > 0. Pn i=1 ai = Pm j=1 bj = 1 b <latexit sha1_base64="LhlbHqBkrxCDCHirUc/UdkhSooo=">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</latexit> <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Couplings: <latexit 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<latexit 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<latexit 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P j Pi,j = ai <latexit 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<latexit 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<latexit 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<latexit 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P i Pi,j = bj <latexit 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P > 0, P1m = a, P>1n = b <latexit 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<latexit 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<latexit 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sha1_base64="p7cKh0q2Fy0W3wTGM7dSK/tQrAw=">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</latexit> Discrete distributions: <latexit 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<latexit 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<latexit 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<latexit 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[Kantorovich 1942] min P nP i,j d(xi, yj)pPi,j ; o <latexit 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<latexit 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<latexit 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George Dantzig Leonid Kantorovitch
  54. Monge (1784): <latexit 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Kantorovitch’s Exact Relaxation min 2Permn n X i=1 Ci, (i) <latexit 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<latexit 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= Pn j=1 yj <latexit 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↵ = Pn i=1 xi <latexit 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<latexit 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<latexit 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  55. Monge (1784): <latexit 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Kantorovitch’s Exact Relaxation min 2Permn n X i=1 Ci, (i) <latexit 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Kantorovitch (1942): <latexit 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(relaxation) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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min P2Bistn n X i=1 n X j=1 Pi,jCi,j <latexit 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<latexit sha1_base64="sdO0FY9u3qW0CR1PS2diO3ogZog=">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</latexit> Bi-stochastic matrices: <latexit 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<latexit 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<latexit 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Bistn def. = P 2 Rn⇥n + ; P1 = 1, P>1 = 1 <latexit 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<latexit 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<latexit 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Permutations “⇢” <latexit 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<latexit 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<latexit 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= Pn j=1 yj <latexit 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↵ = Pn i=1 xi <latexit 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<latexit 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<latexit 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  56. Monge (1784): <latexit 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n! permutations <latexit 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<latexit 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<latexit 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O(n3) algorithm <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Kantorovitch’s Exact Relaxation min 2Permn n X i=1 Ci, (i) <latexit 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<latexit 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Kantorovitch (1942): <latexit 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(relaxation) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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min P2Bistn n X i=1 n X j=1 Pi,jCi,j <latexit 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<latexit sha1_base64="sdO0FY9u3qW0CR1PS2diO3ogZog=">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</latexit> Bi-stochastic matrices: <latexit 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<latexit 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<latexit 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Bistn def. = P 2 Rn⇥n + ; P1 = 1, P>1 = 1 <latexit 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<latexit 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<latexit 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Permutations “⇢” <latexit 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<latexit 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<latexit 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= Pn j=1 yj <latexit 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↵ = Pn i=1 xi <latexit 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<latexit 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<latexit 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  57. Monge (1784): <latexit 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John von Neumann George David Birkhoff n! permutations <latexit 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<latexit 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<latexit 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O(n3) algorithm <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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“Monge , Kantorovitch” <latexit 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<latexit 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<latexit sha1_base64="NNSGSaT1RAGw0E6wwEr1/Kdeyu4=">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</latexit> Theorem: [Birkho↵-von Neumann] <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Kantorovitch’s Exact Relaxation min 2Permn n X i=1 Ci, (i) <latexit 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Kantorovitch (1942): <latexit 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(relaxation) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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min P2Bistn n X i=1 n X j=1 Pi,jCi,j <latexit 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<latexit sha1_base64="sdO0FY9u3qW0CR1PS2diO3ogZog=">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</latexit> Bi-stochastic matrices: <latexit 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<latexit 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<latexit 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Bistn def. = P 2 Rn⇥n + ; P1 = 1, P>1 = 1 <latexit 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<latexit 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<latexit 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Permutations “⇢” <latexit 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<latexit 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<latexit 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= Pn j=1 yj <latexit 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↵ = Pn i=1 xi <latexit 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<latexit 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<latexit sha1_base64="ezP0eoP3WwPzUVfpfgYNSe3Kz5A=">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</latexit>
  58. Extremal points: Birkhoff von Neumann proof equivalent. For this, we

    will make a detour through a more general linear optimization problem of the f for some compact convex set C. We first introduce the notion of extremal points, which are vertices of C Extr(C) := P ; ↑ (Q, R) → C 2, P = Q + R 2 ↘ Q = R . So to show that P / → Extr(C) is su!ces to split P as P = Q+R 2 with Q ≃= R and (Q, R) → C2. the following fundamental result. Proposition 4. If C is compact, then Extr(C) ≃= 0. The fact that C is compact is crucial, for instance, the set (x, y) → R2 + ; xy ↫ 1 has no We can now use this result to show the following fundamental result, namely that th solution to a linear program which is an extremal point. Note that of course, the set of solu non-empty because one minimizes a continuous function on a compact) might not be a sing 11 Figure 1: Left: extremal points of a convex set. Right: the solution of a convex program Proposition 5. If C is compact, then Extr(C) → argmin P→C ↑C, P↓ ↔= ↗. Proof. One consider S := argmin P→C ↑C, P↓. We first note that S is convex (as always fo compact because C is compact and the objective function is continuous so that Extr(S) that Extr(S) ↘ Extr(C). [ToDo: finish] al points of a convex set. Right: the solution of a convex program is a convex set. compact, then Extr(C) → argmin P→C ↑C, P↓ ↔= ↗. := argmin P→C ↑C, P↓. We first note that S is convex (as always for an argmin) and ompact and the objective function is continuous so that Extr(S) ↔= ↗. We will show . [ToDo: finish] em states that the extremal points of bistochastic matrices are the permutation 𝒞 C Argmin Figure 1: Left: extremal points of a convex set. Right: the solut Proposition 5. If C is compact, then Extr(C) → argmin P→C ↑C, P↓ Proof. One consider S := argmin P→C ↑C, P↓. We first note that S Figure 1: Left: extremal points of a convex set. Right: the solution of a convex pro Proposition 5. If C is compact, then Extr(C) → argmin P→C ↑C, P↓ ↔= ↗. Proof. One consider S := argmin P→C ↑C, P↓. We first note that S is convex (as alway compact because C is compact and the objective function is continuous so that Extr( that Extr(S) ↘ Extr(C). [ToDo: finish] The following theorem states that the extremal points of bistochastic matrices matrices. It implies as a corollary that the cost of Monge and Kantorovitch are the share a common solution. Theorem 2 (Birkho! and von Neumann). One has Extr(Bn ) = Pn . Proof. We first show the simplest inclusion Pn ↘ Extr(Bn ). Indeed it follows from the
  59. A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction:

    O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵
  60. A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction:

    O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)).
  61. A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction:

    O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)). p = 1 d = || · || ! min-cost flow, on graphs O(n2 log(n)). W1(↵, ) = min div(u)=↵ R ||u(x)||dx <latexit 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<latexit 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  62. Monge-Amp` ere/Benamou-Brenier, d = || · ||2 2 . A

    Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction: O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)). p = 1 d = || · || ! min-cost flow, on graphs O(n2 log(n)). W1(↵, ) = min div(u)=↵ R ||u(x)||dx <latexit 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  63. Monge-Amp` ere/Benamou-Brenier, d = || · ||2 2 . Semi-discrete:

    Laguerre cells, d = || · ||2 2 . A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction: O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)). p = 1 d = || · || ! min-cost flow, on graphs O(n2 log(n)). W1(↵, ) = min div(u)=↵ R ||u(x)||dx <latexit 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  64. Monge-Amp` ere/Benamou-Brenier, d = || · ||2 2 . Semi-discrete:

    Laguerre cells, d = || · ||2 2 . A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction: O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)). p = 1 d = || · || ! min-cost flow, on graphs O(n2 log(n)). W1(↵, ) = min div(u)=↵ R ||u(x)||dx <latexit 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Entropic regularization: generic d. <latexit 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<latexit 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<latexit 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  65. OT Computational Frameworks https://pythonot.github.io POT: Python Optimal Transport Optimal Transport

    Tools (OTT) https://ott-jax.readthedocs.io https://www.numerical-tours.com https://www.kernel-operations.io
  66. Couplings: general definitions ↵ b <latexit 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<latexit sha1_base64="LhlbHqBkrxCDCHirUc/UdkhSooo=">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</latexit> <latexit

    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<latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="n2zdOYSE8oWxrpoEULZvL+5/PUM=">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</latexit> ⇡ = P i,j Pi,j xi,yj <latexit 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<latexit 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<latexit sha1_base64="41JmsYGA81vfUezwSfJzSu9tJV4=">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</latexit> c(x, y) = d(x, y)p <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Marginals: « » dπ1 = ∫ 𝒴 dπ( ⋅ , y) Using push-forward: where π1 = (P1 )♯ π P1 (x, y) = x ∀f ∈ 𝒞 ( 𝒳 ), ∫ 𝒳 f(x)dπ1 (x) = ∫ 𝒳 × 𝒴 f(x)dπ(x, y) π ∈ 𝒫 ( 𝒳 × 𝒴 ) P ∈ ℝn×m +
  67. Couplings: general definitions ↵ b <latexit 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<latexit sha1_base64="LhlbHqBkrxCDCHirUc/UdkhSooo=">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</latexit> <latexit

    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<latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="n2zdOYSE8oWxrpoEULZvL+5/PUM=">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</latexit> ⇡ = P i,j Pi,j xi,yj <latexit 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<latexit 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<latexit sha1_base64="41JmsYGA81vfUezwSfJzSu9tJV4=">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</latexit> c(x, y) = d(x, y)p <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Marginals: « » dπ1 = ∫ 𝒴 dπ( ⋅ , y) Using push-forward: where π1 = (P1 )♯ π P1 (x, y) = x ∀f ∈ 𝒞 ( 𝒳 ), ∫ 𝒳 f(x)dπ1 (x) = ∫ 𝒳 × 𝒴 f(x)dπ(x, y) π ∈ 𝒫 ( 𝒳 × 𝒴 ) P ∈ ℝn×m + Trivial coupling: , π = α ⊗ β ∫ fdπ = ∫ f(x, y)dα(x)dα(y) the set of couplings is always non empty! → Couplings: {π ∈ 𝒫 ( 𝒳 × 𝒴 ) : π1 = α, π2 = β}
  68. General Kantorovitch Problem Wp(↵, )p def. = min ⇡2M1 +

    (X2) ⇢Z X2 d(x, y)pd⇡(x, y) ; ⇡1 = ↵, ⇡2 = <latexit 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<latexit 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= min X∼α,Y∼β 𝔼 (dp(X, Y)) (probabilistic interpretation)
  69. General Kantorovitch Problem Wp(↵, )p def. = min ⇡2M1 +

    (X2) ⇢Z X2 d(x, y)pd⇡(x, y) ; ⇡1 = ↵, ⇡2 = <latexit 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= min X∼α,Y∼β 𝔼 (dp(X, Y)) (probabilistic interpretation) Discrete case = sub-case of the general problem b <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  70. General Kantorovitch Problem Wp(↵, )p def. = min ⇡2M1 +

    (X2) ⇢Z X2 d(x, y)pd⇡(x, y) ; ⇡1 = ↵, ⇡2 = <latexit 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<latexit 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<latexit 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= min X∼α,Y∼β 𝔼 (dp(X, Y)) (probabilistic interpretation) 60 Entropic Regularization of Optimal Transport 60 Entropic Regularization of Optim ≠ 1 ≠ 1 ≠ 2 Non-optimal <latexit 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<latexit 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<latexit 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Optimal <latexit 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<latexit 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<latexit 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⇡ = ↵ ⌦ <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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(X, Y ) independents <latexit 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<latexit 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⇡ = (Id, T)]↵ <latexit 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<latexit 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Y = T(X) <latexit 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y = T(x) <latexit 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Discrete case = sub-case of the general problem b <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  71. Optimal Transport Distances Wp(↵, ) def. = <latexit sha1_base64="ZLn74A+pY2ZqHm9oqSjbdpXOK7s=">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</latexit> <latexit

    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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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↵n <latexit 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R X fd↵n ! R X fd <latexit 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<latexit 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<latexit 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<latexit 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Convergence in law: <latexit 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<latexit 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↵n *⇤
  72. Optimal Transport Distances Wp(↵, ) def. = <latexit sha1_base64="ZLn74A+pY2ZqHm9oqSjbdpXOK7s=">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</latexit> <latexit

    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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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. . . x1 <latexit 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x2 <latexit 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<latexit 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<latexit 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x3 <latexit 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Wp( xn , x) = d(xn, x) <latexit 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<latexit 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|| xn x ||TV = 2 <latexit 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↵n <latexit 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R X fd↵n ! R X fd <latexit 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<latexit 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<latexit 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<latexit 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Convergence in law: <latexit 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<latexit 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8 f 2 Cc(X), <latexit sha1_base64="vLcn6PBsh2nnzV42KiMCyZwvz5c=">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</latexit> ↵n *⇤ Theorem: <latexit 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<latexit 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<latexit 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Wp is a distance and <latexit 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↵n *⇤ <latexit 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Wp(↵n, ) ! 0 <latexit 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R || · ||pd↵n ! R || · ||pd
  73. Triangular Inequality Proof: Proof of triangular inequality: define R =

    ∑ j S⋅,j,⋅ ∈ U(a, b) (Sub-optimality) (Triangular ineq) (Minkowski ineq)
  74. Application: Central Limit Theorem Central limit theorem: If E(X) =

    0, E(X2) = 1 and (Xi)i i.i.d. ⇠ X Yn def. = X1 + . . . + Xn p n law ! N(0, 1) <latexit sha1_base64="9fWP1tpYm7bF6zn5/shITrF71l0=">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</latexit> µn = Law(Yn) = (µ1 ? . . . ? µ1)(·/ p n) <latexit sha1_base64="/svmzH6GyHaafC1mNus1NaCofgI=">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</latexit> *⇤ µ1 = Law(N(0, 1)) <latexit 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... <latexit 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µ1 <latexit 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µ2 <latexit 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µ3 <latexit 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µ4 <latexit 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µ1
  75. Application: Central Limit Theorem Central limit theorem: If E(X) =

    0, E(X2) = 1 and (Xi)i i.i.d. ⇠ X Yn def. = X1 + . . . + Xn p n law ! N(0, 1) n = 1 n = 4 n = 7 P(Yn 6 t) t <latexit 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</latexit> µn = Law(Yn) = (µ1 ? . . . ? µ1)(·/ p n) <latexit sha1_base64="/svmzH6GyHaafC1mNus1NaCofgI=">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</latexit> *⇤ µ1 = Law(N(0, 1)) <latexit 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... <latexit 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µ1 <latexit 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µ2 <latexit 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µ3 <latexit 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µ4 <latexit 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µ1
  76. Application: Central Limit Theorem Central limit theorem: If E(X) =

    0, E(X2) = 1 and (Xi)i i.i.d. ⇠ X Yn def. = X1 + . . . + Xn p n law ! N(0, 1) n = 1 n = 4 n = 7 P(Yn 6 t) t <latexit 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</latexit> µn = Law(Yn) = (µ1 ? . . . ? µ1)(·/ p n) Carl-Gustav Esseen Theorem: [Berry 1941] [Esseen, 1942] C 6 1/2 <latexit sha1_base64="UncHDA5A9+9Y6Yk1HqgFyJcmRDo=">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</latexit> W1(µn, N(0, 1)) 6 CE(|X|3) p n <latexit sha1_base64="he2QyKAdxt69+efmHYC35sGpVlI=">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</latexit> ! Generalizes to higher dimensions. <latexit sha1_base64="/svmzH6GyHaafC1mNus1NaCofgI=">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</latexit> *⇤ µ1 = Law(N(0, 1)) <latexit 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... <latexit 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µ1 <latexit 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µ2 <latexit 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µ3 <latexit 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µ4 <latexit 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µ1
  77. t <latexit 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<latexit 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Application:

    Gradient Flows Implicit stepping: <latexit 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<latexit 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Limit ⌧ ! 0: <latexit 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@↵ @t = div(↵r(f0(↵))) <latexit 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Felix Otto David Kinderlehrer Richard Jordan <latexit 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Also: mean field analysis of 1-hidden layer neural networks. <latexit 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L3y7Pu5khtaGrTOhTcVrFMOWeXnOcAX8O9L+OvSL9fUS52HZ1HPiKJPvy5KoSdeT25dudJcKeGo7r7aUQ/UEbTxbfW2UR3PS0+V7NJPlX3jFdeSSZmrDwgf8l8j0lEszVWLpo9qH+L7/F1nL0AerPUlq5bsuYNi7jOyFfaBkr9a1iqqbcVzM3IKoViHHMfXf1AqnkPieXceB+NuTT6pkr8ZbpKTT2ZCirLZJc1r/Ra0Hda7q123iZP0G/aKXldNLWsvlyCPtGU0N2PMaeWliDY0TM5iXVVbq0sbxZvx6lqYbbeyUlXX1r4rlvb7bmdV8i875P8mLYwjq3q+7EaFhf3Bdv6/bedtPNSNt7Kgq/qqP9jS76otXdUP2Xbk34XRpRrmG71c500mhVvmWvqWObl7KzQOzHOQPe+pFTM1rFRZ8TcrZHl8Phbx7XG9Gj8TXdW9kzlmDM4nDuSuTXMnbl+vQHH81qZ5BrHnOcVzU2odfAdvS8kp2A+V3I1cjRyVUHdy0XER0yJuU9JoEflBNp7M30eK+6JxBsE+vSGzh4k+iYW306GlJjnk7Yye2FeIbpEa394ts3ejgob5dIe5QTjJlS+fV/bacvSYZBIZGWXn9EUmXeIpN++LEqmEep4/343cpJxI/VZG35bNSNChFcsqXSVk1T5tmhMv64r3nveojvkEykzhrtqZg2M1p7fn0CSd8DyW7Udl3qCoYZO/7HmZIvvRIXmGGIomf5li1SxSsdzYPta1d04qUW5t2thqjlV1urDi5xDnGBqiRTedUG0hpbUoSqFaylNyeeNE1yPK0qVW3iar5H17UxozTLSf5R1DqN3wPeqLynwvcj6R7/ofkB5xN0RLl7mKRzFn9TkPPl8xJZR5N2fwpI1tqWPauZvo2Sic673wlLJPs21T1dXrOKLZfXVfPVD/ALS6kPsrbymmOo9gk9J+LP9+isPsNj97h3D4dqQN9SS7o7FqH6G88yjlib7nzU93J0C1THcno+unHJLXJ7Gf8n31mMYNdbTBUh9H7Ch+QHev+SjjTXPHlKtRuiG/mu4WyHC/VPeSGtqRJHul+CZokca+DfAanSDkexfQDqe1pGtRWhwXk/MqnA70zK3r/Jb5LqTLPa3Ljr4FyJf7Qu+KDO2FvKBScM5XSvbljoP0J0rOY8oY+4LOZsuI2sQLYSr5M0PmJCWXwaYp4/YQ3YtMPp9Ncx6+82yuiveJuSw9hqfcicT6yFMtajiG2m6OHtst780uShxPnWkfZCU3tPMUVzJucypXXH0eqJFFdwWQ1yPtSfxb0QZiuPK5IvvziqWrS7qtq0p3YfnkN4OGdHuisdYq28LbF12toY7XMDwXJRnmmZ0VrTaO4j0nTVtfC6+thXeTVsss/ZGPwhH0NXzj8VFE38U5TT+Fd4nmW0N4rCFUNujMxQsHjZdBKvcyKmgBXU0pT+dlROl5bJo/d+Q+k+0/rdrK7lrF20+PqQZu1q7NAyW/1WA+4fc+en6KvHObx7TS5jvWKd81HSFxfGNOSeH5j1uU9hwettJjfRY8Ue+XJLHRMxp5vFI3VJL5FH8d8J1Q0pPaaSsWJRxfXY+yL9u6HkVak7Elf97NLO+eirvhEBGCsW8byFOIl3YfRnVueix9PKUjTSfU8vczfvkR1Yi4PQqgP1NVd81+phbO3lAshueL5BeA7F/nGRHCnGZh3vn8+ItBmNIHSx5Q/DtT9X69CSnwTh5EbdNbV+/6Yd8wpNEzRmhyJ4T5/SE+fY4tDWet/GfT8NT5ULlmiYu/RcLzPnw2B6Xkc2YvoExDOuv+kfZYLyO8w4AoFG/HsTm0aI6Jdxbg2Pm++qcg1dekm2bhZFZI/kcZKimUIXQGAr01nzUI8bNL8wLapY0tc5Xbn9bAfnbB79U7NdXRepUYInxi9TQnv/HF5haIY+2tWhE1W3WfdczvNRxk7b1890vVjdErgAmNWg9KfsSmEUNhpor3R3P7mAVLJbcYFpHhXYcdVbyDneulE2GdPRrX9QptIS/BPSr7qh7FYk3fzCI6H/XndP80++ezYL/13MqPb8fQi7jPvOa/j5k9kGiAo/ailfrQlzp2XKHxjStW8GPPNbpe/BGOq+Q3PIqxoKuvcsdufrsYKDkfXLzJ2XfSSVaLtjMO7nnEjjK/sMlU+Sxvg9JSqm1jhR36rM/+H7+7vFb8pdfyy9P122s/vX3n0zvLv7infwX2B+pv1d+BLtbUh+oX6iHY5BHI9K/qP9X/qF+f/8v5v5//1/l/c9bvf09jfqRy/53/728BMQhWsw==</latexit> ↵t+⌧ = argmin ↵ 1 2 W2 2 (↵t, ↵) + ⌧f(↵)
  78. Crowd motion with congestion https://www.youtube.com/watch?v=tDQw21ntR64 Tim Whittaker (New Zealand) <latexit

    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C , ↵ ; d↵ dx < T <latexit 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Congestion constraint: <latexit 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r' <latexit 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[Maury, Roudne↵-Chupin, Santambrogio] <latexit sha1_base64="OCaEP+M/QxoslcIqs6+U1e2zcCw=">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</latexit> f(↵) = R 'd↵ + R log(d↵ dx )d↵ + ◆C(↵)
  79. Crowd motion with congestion https://www.youtube.com/watch?v=tDQw21ntR64 Tim Whittaker (New Zealand) <latexit

    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C , ↵ ; d↵ dx < T <latexit 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Congestion constraint: <latexit 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r' <latexit 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[Maury, Roudne↵-Chupin, Santambrogio] <latexit sha1_base64="OCaEP+M/QxoslcIqs6+U1e2zcCw=">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</latexit> f(↵) = R 'd↵ + R log(d↵ dx )d↵ + ◆C(↵)
  80. Wasserstein Barycenters 2 ⌃3 min ↵ P s sWp p

    (↵, ↵s) <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> Wasserstein <latexit 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QB1fFO9bVTH49JTJav0U2WfeMWlZN7M1fuED/mvMekoluayRdNHdQDxffGss0OQB0t9wSole+ygnPqcbIV9oKSvl7WOakfx2IzsQiiXIcfxzS+UiseQeNyd+8G4WpN3qhRPhssK8slISFk2O6dFrd+DusN6d9XrDnGSdsOe0eupqWXt1RwUkbaM5mSMOc28lNGGhklZLqt6a3Vpo3wyXlMLs+1WZqqa2toPxdL+v9tZnfyLDvm/SwvjyKqZL7tTY2G/t53/bdt5Gw91560s6Ka+6ve29H/Vlm7qh2w78q/C6FEJ84lerv0mWemUubY+ZU7O3gr1A4scZM17asVMR9ZbmfE3M2RFfDEW8a1xvRk/E101PZM5pg/OOw7krE1zJu5Az0Bx/NahcQax5znFc1OqHXwGb1vJLtgPlZyNXI8cV1AfFKLjMqZN3Kak0TLy/bw/WTyPFNdF4wiCvXtDRg8TvRMLT6dDS00KyPs5PbGvEN0yNT69W0bvxiUN8+4Oc4JwUshfMa2steXoMcklMjLKyunLXLrEk29eFyVSCfUifz4buUUpkfq9nL4tm5GgSzOWdbpKyKp92jQ7XlYVrz3vUxnzDpSZwlW1MwfHek5vz6FFOuFxLNuPyrhBWcMmfdXzMkX2oyPyDDEUTfoqxbpRpHK+sX6sau+c1KLc2rSx9RzryvTaip9DnGNoiBbddEKlhZRWoiiFSqlIyeWNE12OKEuPanmHrJLX7U2pz5BpP8srhlC74XPUr2vTHRZ8Ip/1PyQ94mqIts5zHY9yyvp9Hry/Ykooc2/24Ekd21AntHI30aNRONZ76cnlgEbbpqqn53FEs7vqoXqk/h5o9SD1N95cTHUawSaV9Vj+9RT7+Wl+9grh8OlIa+pZfkZj3TpCuedeyjN9zpuf7laAapXuVk7XTzkkr09iP+WH6in1G5pog6U+iVhR/IjOXvNRxpPmTijVUeWE/Hq6GyDDw0rZy9vQiiRZK8UnQYs09mmAt2gHIZ+7gHY4bSRdm97FcTEpb8JpT4/cuvZvmW8hXe5oXXb1KUC+1Jd6VWRoLeQl5YJTvlKyLncSpJ8p2Y8pfexL2pstPWoTL4SpFPcMmZ2UnAebpvTbQ3Qvc/l8Ns1p+MyzuSqfJ+ay9BieciYS66NItazhGGrbBXpst7w2uyxxPHWmvZfn3NAuUlzKuc0pX3HluafGFt0lQN6OtCfxb2UbiOHK+4rs5yVLV1d0Wled7sLyyd8MGtHpicZa62wLT1901YYmXsPwvK7IMM/trGy1cRQfOGna+rr22lp4NWm9zNIe+SgcQFvDJx4fRLRdnNK0U3iWaLE2hPsaQmWN9lwcOmgcB6k8yKmgBfQ0pSKd44jcc9+0uO/IvSfbv1u1nZ+1iqefnlAJ3G1cmntK/laDecLvPnp+irxym/u0Uue71i7fFR0hcXxjdknh/o979O4lXGylJ3oveKL+riKJjZ5Rz+OVuqOS3Kf4y4DPhJKW1H63ZFHC/tXtKPuyretJpDUZW/KnXc/T7qi4Ew4RIRj7tIEihXhpd6FX56bH0sdTOtB0QjV/N+dX7FGNiduTAPoLVXfW7Bfq2tkaisXweJH8BSD7r/OMCWF2szDvYnr8i0H4ZgCWPKT4d6aa/fUmpMAreRC1SXc9veqHfcOIes8YocmZEObvD/Huc6xpOGrl35uGu85HyjVKXP5bJDzuw3tzUEreZ3YIeRrRXvePtMc6jvAOQ6JQPh3H5tCmMSZeWYB954fqn4JUX5NuWqWdWSH5n+SopJSH0B4I9Na81yDEz87NIdRLG1vlKqc/rYD9bIPfa7Zrqqv1KjFEeMfqWUF+44vNKRAn2lu1I0q27jzrmL/XsJfX9+rZL3UnRi8BJtRr3av4EZtGDIWZKp8fzfVjFsyVnGJYRoZXHXZV+Qx2LpduhHX2qV/XL9WFogQPKO/LuheLJX03j+h81F/S+dPsn8+D7dZLKz3enUAr4t7zWvweM3og0QBH7WUr9aGvdOy4RP0bV6zgx15odLP4IxxXyd/wKMeCrrbKHbv57WKoZH9w+SRn304nmS3CMYyFk3cXV8p/k7V6c7B6/9f3Vz5fXfzNA/3nWn+ifq7+BoReUR+q36jHYDwHxO5f1L+qf7v464uPL9Yu1jnpj3+kMX+lCv8utv8HikgqTg==</latexit> <latexit 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</latexit> <latexit 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</latexit> 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</latexit> 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</latexit> 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</latexit> 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</latexit> <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> 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</latexit> 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↵2 <latexit 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<latexit 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Martial Agueh Barycenters of measures (↵s)S s=1 : <latexit 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</latexit> 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</latexit> P s s = 1 <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> <latexit sha1_base64="NrvueCyY/slmsn9VM3LdPoErJ0w=">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</latexit> ↵? 2 argmin ↵ P s sWp p (↵, ↵s) <latexit 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</latexit> <latexit 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</latexit> 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</latexit> 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</latexit> <latexit sha1_base64="YAH1dIwLCmW2H0cSZCl/xE4tkjM=">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</latexit> Guillaume Carlier
  81. Wasserstein Barycenters 2 ⌃3 min ↵ P s sWp p

    (↵, ↵s) <latexit 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</latexit> <latexit 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vTLJXWs0/Ao6jlR9OnXRSl0xevJrSvXO9ebcFT3UG2rR+oQ6viWeteojselJ0pW6afKPvGKS8m8makPCR/yXyPSUSzNVYumj2of4vviWWdHIA+W+pJVSvbYQTn1OdkK+0BJXy1rFdW24rEZ2YVQLkOO4+tfKBWPIfG4O/eDcbUm71QpngyXFeSTkZCybHZOi1q/A3WH9e6q123iJO2GPaPXVRPL2hdzUETaMpqTMWY081JGGxomZbmsqq3VpY3yyXh1Lcy2W5mpqmtr3xdL+/9uZ1XyLzvk/zYtjCOrer7sVoWF/cF2/rdt51081K13sqDr+qo/2NL/VVu6rh+y7ci/CqNLJcwnern2m2SlU+Za+pQ5OXsr1A8scpA176kVMzWstzLjb2bIivhiLOJb43o9fia6qnsmc0wfnHccyFmb5kzcvp6B4vitTeMMYs8ziucmVDv4DN6Wkl2wHys5G7kaOVpAfVSIjsuYFnGbkEbLyA/z/mTxPFJcF40jCPbuDRk9TPROLDydDi01KSDv5vTEvkJ0y9T49G4ZvRuVNMy7O8wJwkkhf8W0staWo8ckl8jIKCunL3PpEk++eV2USCXUi/z5bOQmpUTqd3L6tmxGgg7NWFbpKiGr9mnT7HhZV7z2vEdlzDtQpgpX1U4dHKs5vTuHJumEx7FsPyrjBmUNm/SLnpcpsh8dkmeIoWjSL1KsGkUq5xvrx7r2zkklyq1NG1vNsapM51b8HOIcQ0O06KYTKi2ktBZFKVRKRUoub5zockRZulTL22SVvG5vQn2GTPtZXjGE2g2foz6vTHdU8Il81v+A9IirIVo6z1U8yimr93nw/ooJocy92YMndeyBOqGVu4kejcKx3ktPLvs02jZRXT2PI5rdUw/VI/VLoNWF1F97czHRaQSbLKzH8q+nOMhP87NXCIdPR9pQz/IzGqvWEco991Ke6XPe/HS3A1QX6W7ndP2UQ/L6JPZTfqieUr+hjjZY6pOIFcWP6Ow1H2U8ae6EUjUWTsivpvsAZHi4UPbyNrQiSdZK8UnQIo19GuAN2kHI5y6gHU5qSdeid3FcTMrrcNrXI7eu/VvmW0iXu1qXHX0KkC/1pV4VGVoLeUm54JSvlKzLHQfpZ0r2Y0of+5L2ZkuP2sQLYSrFPUNmJyXnwaYp/fYQ3ctcPp9Ncxo+82ymyueJuSw9hqecicT6KFItaziG2k6BHtstr80uSxxPnWnv5zk3tIsUV3JuM8pXXHnuq5FFdwWQNyPtSfxb2QZiuPK+Ivt5xdLVFZ3WVaW7sHzyN4OGdHqisdYq28LTF121oY7XMDznCzLMcjsrW20cxftOmra+5l5bC68mrZZZ2iMfhUNoa/jE48OItotTmnYKzxIt1oZwX0OobNCeiyMHjeMglfs5FbSArqZUpHMckXvumxb3Hbn3ZPt3q7bys1bx9NMTKoHbtUtzX8nfajBP+N1Hz0+RV25zn1bqfMfa5bumIySOb8wuKdz/cYfevYSLrfRE7wVP1C8WJLHRU+p5vFK3VJL7FH8Z8JlQ0pLa71YsSti/uhllX7Z1PYm0JmNL/rSbedpdFXfCISIEY582UKQQL+0e9Orc9Fj6eEqHmk6o5u/l/Io9qhFxexJAf6Gqzpr9Qs2draFYDI8XyV8Asv86z4gQZjcL8y6mx78YhG/6YMkDin+nqt5fb0IKvJIHUVt019Wrftg3DKn3jBGanAlh/v4Q7z7HmoajVv69abjrfKhco8Tlv0XC4z68Nwel5H1mR5CnIe11/0R7rOMI7zAgCuXTcWwOLRpj4pUF2Hd+qP4xSPU16aZZ2pkVkv9JjkpKeQjtgUBvzXsNQvzs3BxBvbSxi1zl9Kc1sJ8d8Hv1dk11tF4lhgjvWD0ryG98sTkF4kR7q1ZEyVadZx3z9xr28/q+ePZL1YnRK4AJ9Vr3F/yITSOGwlSVz4/m+jEN5kpOMSwjw6sOO6p8BjuXSyfCOnvUr+uV6kJRgvuU91Xdi8WSvp1HdD7qL+n8afbP58F266WVHu9OoBVx73ktfo8ZPZBogKP2spX60Fc6dlyh/o0rVvBjLzS6XvwRjqvkb3iUY0FXW+WO3fx2MVCyP7h8krNvp5PMFuEYxtLJ+8tr5b/JunhzuH7313fXPl9f/u19/edaf6z+Wv0tCL2mPla/VY/BeA6B3T+rf1f/of7z4t5F+6J78YaT/vAHGvMzVfh3MfkfbFM5bQ==</latexit> <latexit 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</latexit> <latexit 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vTLJXWs0/Ao6jlR9OnXRSl0xevJrSvXO9ebcFT3UG2rR+oQ6viWeteojselJ0pW6afKPvGKS8m8makPCR/yXyPSUSzNVYumj2of4vviWWdHIA+W+pJVSvbYQTn1OdkK+0BJXy1rFdW24rEZ2YVQLkOO4+tfKBWPIfG4O/eDcbUm71QpngyXFeSTkZCybHZOi1q/A3WH9e6q123iJO2GPaPXVRPL2hdzUETaMpqTMWY081JGGxomZbmsqq3VpY3yyXh1Lcy2W5mpqmtr3xdL+/9uZ1XyLzvk/zYtjCOrer7sVoWF/cF2/rdt51081K13sqDr+qo/2NL/VVu6rh+y7ci/CqNLJcwnern2m2SlU+Za+pQ5OXsr1A8scpA176kVMzWstzLjb2bIivhiLOJb43o9fia6qnsmc0wfnHccyFmb5kzcvp6B4vitTeMMYs8ziucmVDv4DN6Wkl2wHys5G7kaOVpAfVSIjsuYFnGbkEbLyA/z/mTxPFJcF40jCPbuDRk9TPROLDydDi01KSDv5vTEvkJ0y9T49G4ZvRuVNMy7O8wJwkkhf8W0staWo8ckl8jIKCunL3PpEk++eV2USCXUi/z5bOQmpUTqd3L6tmxGgg7NWFbpKiGr9mnT7HhZV7z2vEdlzDtQpgpX1U4dHKs5vTuHJumEx7FsPyrjBmUNm/SLnpcpsh8dkmeIoWjSL1KsGkUq5xvrx7r2zkklyq1NG1vNsapM51b8HOIcQ0O06KYTKi2ktBZFKVRKRUoub5zockRZulTL22SVvG5vQn2GTPtZXjGE2g2foz6vTHdU8Il81v+A9IirIVo6z1U8yimr93nw/ooJocy92YMndeyBOqGVu4kejcKx3ktPLvs02jZRXT2PI5rdUw/VI/VLoNWF1F97czHRaQSbLKzH8q+nOMhP87NXCIdPR9pQz/IzGqvWEco991Ke6XPe/HS3A1QX6W7ndP2UQ/L6JPZTfqieUr+hjjZY6pOIFcWP6Ow1H2U8ae6EUjUWTsivpvsAZHi4UPbyNrQiSdZK8UnQIo19GuAN2kHI5y6gHU5qSdeid3FcTMrrcNrXI7eu/VvmW0iXu1qXHX0KkC/1pV4VGVoLeUm54JSvlKzLHQfpZ0r2Y0of+5L2ZkuP2sQLYSrFPUNmJyXnwaYp/fYQ3ctcPp9Ncxo+82ymyueJuSw9hqecicT6KFItaziG2k6BHtstr80uSxxPnWnv5zk3tIsUV3JuM8pXXHnuq5FFdwWQNyPtSfxb2QZiuPK+Ivt5xdLVFZ3WVaW7sHzyN4OGdHqisdYq28LTF121oY7XMDznCzLMcjsrW20cxftOmra+5l5bC68mrZZZ2iMfhUNoa/jE48OItotTmnYKzxIt1oZwX0OobNCeiyMHjeMglfs5FbSArqZUpHMckXvumxb3Hbn3ZPt3q7bys1bx9NMTKoHbtUtzX8nfajBP+N1Hz0+RV25zn1bqfMfa5bumIySOb8wuKdz/cYfevYSLrfRE7wVP1C8WJLHRU+p5vFK3VJL7FH8Z8JlQ0pLa71YsSti/uhllX7Z1PYm0JmNL/rSbedpdFXfCISIEY582UKQQL+0e9Orc9Fj6eEqHmk6o5u/l/Io9qhFxexJAf6Gqzpr9Qs2draFYDI8XyV8Asv86z4gQZjcL8y6mx78YhG/6YMkDin+nqt5fb0IKvJIHUVt019Wrftg3DKn3jBGanAlh/v4Q7z7HmoajVv69abjrfKhco8Tlv0XC4z68Nwel5H1mR5CnIe11/0R7rOMI7zAgCuXTcWwOLRpj4pUF2Hd+qP4xSPU16aZZ2pkVkv9JjkpKeQjtgUBvzXsNQvzs3BxBvbSxi1zl9Kc1sJ8d8Hv1dk11tF4lhgjvWD0ryG98sTkF4kR7q1ZEyVadZx3z9xr28/q+ePZL1YnRK4AJ9Vr3F/yITSOGwlSVz4/m+jEN5kpOMSwjw6sOO6p8BjuXSyfCOnvUr+uV6kJRgvuU91Xdi8WSvp1HdD7qL+n8afbP58F266WVHu9OoBVx73ktfo8ZPZBogKP2spX60Fc6dlyh/o0rVvBjLzS6XvwRjqvkb3iUY0FXW+WO3fx2MVCyP7h8krNvp5PMFuEYxtLJ+8tr5b/JunhzuH7313fXPl9f/u19/edaf6z+Wv0tCL2mPla/VY/BeA6B3T+rf1f/of7z4t5F+6J78YaT/vAHGvMzVfh3MfkfbFM5bQ==</latexit> <latexit 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</latexit> Wasserstein <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> 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nqkDqCOb6q3jep4XHqqZJV+quwTr7iUzJu5ep/wIf81Jh3F0ly2aPqoDiC+L551dgjyYKkvWKVkjx2UU5+TrbAPlPT1stZR7Sgem5FdCOUy5Di++YVS8RgSj7tzPxhXa/JOleLJcFlBPhkJKctm57So9XtQd1jvrnrdIU7Sbtgzej01tay9moMi0pbRnIwxp5mXMtrQMCnLZVVvrS5tlE/Ga2phtt3KTFVTW/uhWNrvu53Vyb/okP+7tDCOrJr5sjs1FvYH2/lt287beKg7b2VBN/VVf7Cl31Vbuqkfsu3IvwqjRyXMJ3q59ptkpVPm2vqUOTl7K9QPLHKQNe+pFTMdWW9lxt/MkBXxxVjEt8b1ZvxMdNX0TOaYPjjvOJCzNs2ZuAM9A8XxW4fGGcSe5xTPTal28Bm8bSW7YD9UcjZyPXJcQX1QiI7LmDZxm5JGy8j38/5k8TxSXBeNIwj27g0ZPUz0Tiw8nQ4tNSkg7+f0xL5CdMvU+PRuGb0blzTMuzvMCcJJIX/FtLLWlqPHJJfIyCgrpy9z6RJPvnldlEgl1Iv8+WzkFqVE6vdy+rZsRoIuzVjW6Sohq/Zp0+x4WVW89rxPZcw7UGYKV9XOHBzrOb09hxbphMexbD8q4wZlDZv0Vc/LFNmPjsgzxFA06asU60aRyvnG+rGqvXNSi3Jr08bWc6wr02srfg5xjqEhWnTTCZUWUlqJohQqpSIllzdOdDmiLD2q5R2ySl63N6U+Q6b9LK8YQu2Gz1G/rk13WPCJfNb/kPSIqyHaOs91PMop6/d58P6KKaHMvdmDJ3VsQ53Qyt1Ej0bhWO+lJ5cDGm2bqp6exxHN7qqH6pH6FdDqQepvvLmY6jSCTSrrsfzrKfbz0/zsFcLh05HW1LP8jMa6dYRyz72UZ/qcNz/drQDVKt2tnK6fckhen8R+yg/VU+o3NNEGS30SsaL4EZ295qOMJ82dUKqjygn59XQ3QIaHlbKXt6EVSbJWik+CFmns0wBv0Q5CPncB7XDaSLo2vYvjYlLehNOeHrl17d8y30K63NG67OpTgHypL/WqyNBayEvKBad8pWRd7iRIP1OyH1P62Je0N1t61CZeCFMp7hkyOyk5DzZN6beH6F7m8vlsmtPwmWdzVT5PzGXpMTzlTCTWR5FqWcMx1LYL9NhueW12WeJ46kx7L8+5oV2kuJRzm1O+4spzT40tukuAvB1pT+LfyjYQw5X3FdnPS5aurui0rjrdheWT3wwa0emJxlrrbAtPX3TVhiZew/C8rsgwz+2sbLVxFB84adr6uvbaWng1ab3M0h75KBxAW8MnHh9EtF2c0rRTeJZosTaE+xpCZY32XBw6aBwHqTzIqaAF9DSlIp3jiNxz37S478i9J9u/W7Wdn7WKp5+eUAncbVyae0p+q8E84XcfPT9FXrnNfVqp811rl++KjpA4vjG7pHD/xz169xIuttITvRc8UX9fkcRGz6jn8UrdUUnuU/xlwGdCSUtqv1uyKGH/6naUfdnW9STSmowt+dOu52l3VNwJh4gQjH3aQJFCvLS70Ktz02Pp4ykdaDqhmr+b8yv2qMbE7UkA/YWqO2v2C3XtbA3FYni8SH4ByP51njEhzG4W5l1Mj78YhG8GYMlDin9nqtmvNyEFXsmDqE266+lVP+wbRtR7xghNzoQwvz/Eu8+xpuGolX9vGu46HynXKHH5t0h43If35qCUvM/sEPI0or3uH2mPdRzhHYZEoXw6js2hTWNMvLIA+84P1b8Eqb4m3bRKO7NC8j/JUUkpD6E9EOitea9BiJ+dm0Oolza2ylVOf1oB+9kGv9ds11RX61ViiPCO1bOC/MYXm1MgTrS3akeUbN151jG/17CX1/fq2S91J0YvASbUa92r+BGbRgyFmSqfH831YxbMlZxiWEaGVx12VfkMdi6XboR19qlf1y/VhaIEDyjvy7oXiyV9N4/ofNRf0vnT7J/Pg+3WSys93p1AK+Le81r8HjN6INEAR+1lK/Whr3TsuET9G1es4MdeaHSz+CMcV8lveJRjQVdb5Y7d/HYxVLI/uHySs2+nk8wW4RjGwsm7iyvl32St3hys3v/n+yufL6ufqr9WfwuyrqgP1b+qx2AzB8Tl39V/qP+8+KuLjy/W+Odcf/wj/buuv1CF/y7W/x/6rije</latexit> 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</latexit> 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</latexit> 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</latexit> <latexit 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</latexit> <latexit 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</latexit> <latexit 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QB1fFO9bVTH49JTJav0U2WfeMWlZN7M1fuED/mvMekoluayRdNHdQDxffGss0OQB0t9wSole+ygnPqcbIV9oKSvl7WOakfx2IzsQiiXIcfxzS+UiseQeNyd+8G4WpN3qhRPhssK8slISFk2O6dFrd+DusN6d9XrDnGSdsOe0eupqWXt1RwUkbaM5mSMOc28lNGGhklZLqt6a3Vpo3wyXlMLs+1WZqqa2toPxdL+v9tZnfyLDvm/SwvjyKqZL7tTY2G/t53/bdt5Gw91560s6Ka+6ve29H/Vlm7qh2w78q/C6FEJ84lerv0mWemUubY+ZU7O3gr1A4scZM17asVMR9ZbmfE3M2RFfDEW8a1xvRk/E101PZM5pg/OOw7krE1zJu5Az0Bx/NahcQax5znFc1OqHXwGb1vJLtgPlZyNXI8cV1AfFKLjMqZN3Kak0TLy/bw/WTyPFNdF4wiCvXtDRg8TvRMLT6dDS00KyPs5PbGvEN0yNT69W0bvxiUN8+4Oc4JwUshfMa2steXoMcklMjLKyunLXLrEk29eFyVSCfUifz4buUUpkfq9nL4tm5GgSzOWdbpKyKp92jQ7XlYVrz3vUxnzDpSZwlW1MwfHek5vz6FFOuFxLNuPyrhBWcMmfdXzMkX2oyPyDDEUTfoqxbpRpHK+sX6sau+c1KLc2rSx9RzryvTaip9DnGNoiBbddEKlhZRWoiiFSqlIyeWNE12OKEuPanmHrJLX7U2pz5BpP8srhlC74XPUr2vTHRZ8Ip/1PyQ94mqIts5zHY9yyvp9Hry/Ykooc2/24Ekd21AntHI30aNRONZ76cnlgEbbpqqn53FEs7vqoXqk/h5o9SD1N95cTHUawSaV9Vj+9RT7+Wl+9grh8OlIa+pZfkZj3TpCuedeyjN9zpuf7laAapXuVk7XTzkkr09iP+WH6in1G5pog6U+iVhR/IjOXvNRxpPmTijVUeWE/Hq6GyDDw0rZy9vQiiRZK8UnQYs09mmAt2gHIZ+7gHY4bSRdm97FcTEpb8JpT4/cuvZvmW8hXe5oXXb1KUC+1Jd6VWRoLeQl5YJTvlKyLncSpJ8p2Y8pfexL2pstPWoTL4SpFPcMmZ2UnAebpvTbQ3Qvc/l8Ns1p+MyzuSqfJ+ay9BieciYS66NItazhGGrbBXpst7w2uyxxPHWmvZfn3NAuUlzKuc0pX3HluafGFt0lQN6OtCfxb2UbiOHK+4rs5yVLV1d0Wled7sLyyd8MGtHpicZa62wLT1901YYmXsPwvK7IMM/trGy1cRQfOGna+rr22lp4NWm9zNIe+SgcQFvDJx4fRLRdnNK0U3iWaLE2hPsaQmWN9lwcOmgcB6k8yKmgBfQ0pSKd44jcc9+0uO/IvSfbv1u1nZ+1iqefnlAJ3G1cmntK/laDecLvPnp+irxym/u0Uue71i7fFR0hcXxjdknh/o979O4lXGylJ3oveKL+riKJjZ5Rz+OVuqOS3Kf4y4DPhJKW1H63ZFHC/tXtKPuyretJpDUZW/KnXc/T7qi4Ew4RIRj7tIEihXhpd6FX56bH0sdTOtB0QjV/N+dX7FGNiduTAPoLVXfW7Bfq2tkaisXweJH8BSD7r/OMCWF2szDvYnr8i0H4ZgCWPKT4d6aa/fUmpMAreRC1SXc9veqHfcOIes8YocmZEObvD/Huc6xpOGrl35uGu85HyjVKXP5bJDzuw3tzUEreZ3YIeRrRXvePtMc6jvAOQ6JQPh3H5tCmMSZeWYB954fqn4JUX5NuWqWdWSH5n+SopJSH0B4I9Na81yDEz87NIdRLG1vlKqc/rYD9bIPfa7Zrqqv1KjFEeMfqWUF+44vNKRAn2lu1I0q27jzrmL/XsJfX9+rZL3UnRi8BJtRr3av4EZtGDIWZKp8fzfVjFsyVnGJYRoZXHXZV+Qx2LpduhHX2qV/XL9WFogQPKO/LuheLJX03j+h81F/S+dPsn8+D7dZLKz3enUAr4t7zWvweM3og0QBH7WUr9aGvdOy4RP0bV6zgx15odLP4IxxXyd/wKMeCrrbKHbv57WKoZH9w+SRn304nmS3CMYyFk3cXV8p/k7V6c7B6/9f3Vz5fXfzNA/3nWn+ifq7+BoReUR+q36jHYDwHxO5f1L+qf7v464uPL9Yu1jnpj3+kMX+lCv8utv8HikgqTg==</latexit> <latexit 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</latexit> <latexit 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</latexit> <latexit 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</latexit> Euclidean <latexit 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↵2 <latexit 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<latexit 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Martial Agueh Barycenters of measures (↵s)S s=1 : <latexit 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</latexit> 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</latexit> P s s = 1 <latexit 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</latexit> <latexit 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</latexit> <latexit 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Xpy68qV5koJR3WP1bZ6og6hjW+pd43qeF56omSXfqrsG6+4lkzKTL1P+JD/GpGOYmkuWzR9VPsQ3xfvOjsCebDWF6xasucOyrnPyVbYB0r+almrqLYVz83IKYRyHXIcX/9BqXgOiefdeRyMuzX5pErxZrisIJ/MhJRls0ta1PoDaDusd1e7bhMn6TfsFb2umljWPl+CItKW0dyMMaOVlzLa0DA5y3VVba0ubZRvxqtrYbbdykpVXVv7oVja/3c7q5J/0SH/d2lhHFnV82X3Kizs17bzv2077+Kh7r2TBd3UV/3alv6v2tJN/ZBtR/5dGF2qYb7Ry3XeJCvdMtfSt8zJ3VuhcWCRg+x5T62YqWGlyoq/WSEr4ouxiG+P6834meiq7p3MMWNwPnEgd22aO3H7egWK47c2zTOIPc8onptQ6+A7eFtKTsF+qORu5GrkaA71QSE6LmNaxG1CGi0j38/Hk8X7SHFfNM4g2Kc3ZPYw0Sex8HY6tNSkgHyY0xP7CtEtU+Pbu2X2blTSMJ/uMDcIJ4XyFfPKXluOHpNcIiOj7Jy+zKVLPOXmfVEilVAv8ue7kZuUE6k/yOnbshkJOrRiWaWrhKzap01z4mVV8d7zHtUxn0CZKtxVO3VwrOb07hyapBOex7L9qMwblDVs8s97XqbIfnRIniGGosk/T7FqFqlcbmwfq9o7J5UotzZtbDXHqjq9tuLnEOcYGqJFN51QbSGllShKoVoqUnJ540TXI8rSpVbeJqvkfXsTGjNk2s/yjiHUbvge9evKfEcFn8h3/Q9Ij7gboqXLXMWjnLP6nAefr5gQyrybM3jSxjbVCe3cTfRsFM71XnpK2afZtonq6nUc0eyeeqyeqL8CWl3I/Y23FBOdR7DJ3H4s/36Kg/w2P3uHcPh2pDX1Ir+jsWofobzzKOWFvufNT3c7QHWe7nZO1085JK9PYj/lx+o5jRvqaIOlPonYUfyE7l7zUcab5k4oV2Puhvxqupsgw+O5upfU0I4k2SvFN0GLNPZtgLfpBCHfu4B2OKklXYvS4riYnDfhtK9nbl3nt8x3IV3ual129C1AvtyXeldkaC/kJZWCc75Wsi93HKSfKTmPKWPsSzqbLSNqEy+EqRTPDJmTlFwGm6aM20N0L3P5fDbNefjOs5kq3yfmsvQYnnInEuujSLWs4RhqOwV6bLe8N7sscTx1pr2fl9zQLlJcyrnNqFxx9bmvRhbdJUDejbQn8W9lG4jhyueK7M9Llq6u6LauKt2F5ZO/GTSk2xONtVbZFt6+6GoNdbyG4Xk9J8Mst7Oy1cZRXHfStPV17bW18G7SapmlP/JROIS+hm88Pozouzin6afwLtFiawiPNYTKGp25OHLQOA5SWc+poAV0NaUineOI0vPYtHjuyH0m239atZXftYq3n55QDdyvXZv7Sv5Wg/mE3/vo+Snyzm0e00qb71infFd0hMTxjTklhec/HlDaK3jYSk/0WfBE/eWcJDZ6SiOP1+qeSnKf4q8DvhNKelI7bcmihOOru1H2ZVvXs0hrMrbkz7uR591VcTccIkIw9m0DRQrx0u7BqM5Nj6WPp3So6YRa/l7OrziiGhG3ZwH0F6rqrtkv1LWzNxSL4fki+QtA9l/nGRHCnGZh3sX8+BeDMKUPljyg+Heq6v31JqTAO3kQtUVvXb3rh33DkEbPGKHJnRDm7w/x6XNsaThr5T+bhqfOh8o1S1z+WyQ878Nnc1BKPmd2BGUa0ln3j7THOo7wDgOiUL4dx+bQojkm3lmAY+fH6u+DVN+Qbpqlk1kh+Z/lqKRUhtAZCPTWfNYgxM8uzRG0Sxs7z1Vuf1oB+9kBv1fv1FRH61ViiPCJ1bOC/MYXm1sgTrS3akXUbNV91jF/r2E/b+/zd79U3Ri9BJjQqHV/zo/YNGIoTFX5/mhuH9NgqeQWwzIyvOuwo8p3sHO9dCKss0fjul6pLRQlWKeyL+tRLNb0/Tyi81F/RfdPs38+D/Zbr6z8+HYCvYj7zGvx+5jZA4kGOGovW6kPfaVjxyUa37hiBT/2QqPrxR/huEr+hkc5FnT1Ve7YzW8XAyXng8s3OftOOslqEc5hLJzcWlwp/03W+ZfD1Yd/93Dls5XFj9cV//uJ+hP15yD0ivpQfayegvEcArsL9Y/qn9W/XPzpxfrF04tnnPXHP9KYP1aFfxf7/wPm7i97</latexit> <latexit 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</latexit> <latexit sha1_base64="NrvueCyY/slmsn9VM3LdPoErJ0w=">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</latexit> ↵? 2 argmin ↵ P s sWp p (↵, ↵s) <latexit 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</latexit> <latexit 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</latexit> 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</latexit> 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</latexit> <latexit 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</latexit> Guillaume Carlier
  82. MRI Data Procesing [with A. Gramfort] L2 barycenter W2 2

    barycenter Ground cost c = dM : geodesic on cortical surface M.
  83. Bag of Words Dist(D1, D2) = W2(↵, ) <latexit sha1_base64="QCSRmVm3aqRzvp3CFa8R51ft4uA=">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</latexit>

    <latexit 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<latexit 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Obama speaks to the media in Illinois The president greets the press in Chicago Document D1 <latexit 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<latexit 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<latexit 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Document D2 <latexit 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<latexit 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<latexit 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Obama speaks media Illinois president greets Chicago press word2vec embedding [Mikolov et al. 2013] <latexit 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<latexit 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<latexit 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Word mover’s distance: [Kusner et al 2015] <latexit 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<latexit 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  84. Density Fitting and Generative Models ✓ Parametric model: ✓ 7!

    ↵✓ <latexit 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<latexit 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<latexit 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↵✓ <latexit 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<latexit sha1_base64="/IX3qCorxR4bVe9DcVqsRyK1ko8=">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</latexit> Observations: def. = 1 n Pn i=1 xi <latexit 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<latexit 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  85. Density Fitting and Generative Models ✓ Parametric model: ✓ 7!

    ↵✓ <latexit 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<latexit 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<latexit 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↵✓ <latexit 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<latexit sha1_base64="/IX3qCorxR4bVe9DcVqsRyK1ko8=">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</latexit> Observations: def. = 1 n Pn i=1 xi <latexit 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<latexit 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Density fitting: Maximum likelihood (MLE) d↵✓(x) = ⇢✓(x)dx <latexit 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  86. Density Fitting and Generative Models ✓ Parametric model: ✓ 7!

    ↵✓ <latexit 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<latexit 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<latexit 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↵✓ <latexit 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<latexit sha1_base64="/IX3qCorxR4bVe9DcVqsRyK1ko8=">AAA/fHiczVvddhu3EUbSv1j9s9vLXnRbxY2dOj6y6tO0J6d1bEmWFdOWbIm2kzB2+bOiNl5x6V1Ssswyb9Lb9qKP0CfpG9SP0Kt2ZgAssCR2B3DTcyIcSVgQ38xgAMwPsOyN06SYrK398623v/Xt73z3e++cW/n+D374ox+fv/CTR0U2zftxu5+lWf6k1y3iNBnF7UkySeMn4zzuHvfS+HHv+QZ+/vgkzoskGx1MzsbxF8fd4Sg5TPrdCTQ9O39h1iEis146jeedXjx/dn517eoa/UTLlWuqsirUz1524efvi44YiEz0xVQci1iMxATqqeiKAsrn4ppYE2No+0LMoC2HWkKfx2IuVgA7hV4x9OhC63P4O4Snz1XrCJ6RZkHoPnBJ4TcHZCQuAiaDfjnUkVtEn0+JMrbW0Z4RTZTtDP73FK1jaJ2II2jlcLqnP24ArYcgG2qmecwT6Pc7GmsCvcfUglroK25T0h6OMLJGPwEKY2jD+gA+z6HeJ6Sej4gwBekI56BLn/+LemIrPvdV36l4TaP5pujvm6eXiwElEjvivtgQLdEWm2JL7JO8zWWFcBswjjHoOAfJh6AhlPYSSHMZ/q/DnloTH0JtG2TsUZ8YxhKJPfh/RvKvKFkjcU/cFAfiDvG+BPV7ULscME9cT722C5oN/3WzwqyynGbkrFGCCY1/ShYgFy8b++LaGajZPKT1UKgd2TynUoMb4qHYbZw/5DwC+qdkiY5Jg8hxBu1DkAlXaAr80CbiWv67+EqsQv0r8Q+1jiOQK1cr+4joySd/mn+CgjTfgzIX54hmG6ReKUcZwZOcgaxc/V1xQnsjIks+hc/kXkpp7Y2oV9Po7kOZU02vmh6UGbXOG5EbUFzIDRa5DcWF3GaRLSguZItF7kFxIfcUsgn7AIoL+4Dl+hCKC/mQRR5AcSEPWOQjKC7kIxb5GRQX8jMWeRuKC3mbRd6F4kLeZZFtKC5km0VuQXEhtxSyfq+hXcuITsLsq5tQr/JAP5VCy01WvltkY13YWx67sl+D5fflJvx3Yzc9dBrXYLc8Vs9hDZZfP9tg5dxY3prcIR/pwt5hsTuwAtzYHRb7ifiyBvuJx355XoPld0yL/I0Ly9vPe/Dkxt5jsfeh5sbyXmYXWtzYXQ+bP67B7rHYB+JFDdbH6uc1WN7u71Ms5sLue/iMSQ2W9xptiB3cWN6ePoIYxI3lfc5jaHVjH7PYJxQ1urBPWOynFJ26sJ96+MlXNVjtKWX0PqQYMIYd20StW+5KrI2BWpfhn5a+BWvoowYsZlhihoQ5ZhHbJWLbE9EqES1vuYrSjhYUsfJc9kvEvieiV/omrE3Y/oOy/4ByMx6xWSI2FxBNWQDOtR7LCUUXuoVDTkrPhTWfMWWl/cZarNZDs+XViN0KQq7tI1r5VyhXx0xmQHlrPbWj0sdLZETPTYhTyvX0KDUPHjcprYKNesmieg5Uj0WdOVBnLGrqQE1Z1IkDdcKizM63cR2PFWD0j3Mxoyed+3NnKdWzi13wuFvg/bBlF/77nKU0Z+V4IoCeUmfPxhbnUJtRJm0yu03KkeVJQwySyZ676owJn/BscqZ2nbTD89KXR0KfePrTSUieYUkH48WIdlQYnbvUMqf4TtbC8HfKna9rYfgt0vic4nhZC8NPlPSTN5D9QGEP3gC7D/tprLRv6qE05BmKpKHrnG3eKe0mnle+pJ0j20L5b1BN6sDUw2gU1hiKyhhCaBhdFpYuw6hgjCRjW12LgkcyUtmtqYfKkJGvHCk5zFPozGCfgZoZXQ+jsQdx1QZl1jOrHrpCx+VoTD2MxiMhz9bnFK/rehiNIT1LfZh6GA08U+mqbN7UQ603akBmyKauY5acohh94pyQ924+S7Ej8mUfgycqT8sIvpmSiTzr6fRKP9Ms0aJ1CZEDvf/UipCqNGZinc1+pAyTiu9dpmP8L2q+BVqMYNfKc33uTDoFCfWJQUyn5E+JWjOmOjKNW2dxaEkOF1Ad1TphYznDV57pVNueUSuXNZnRGj12yM4WtPbGFLG1SLOcHlq1M1xHkdNQq6Ihnl6I7l7RDs4WtL/G4sYLiHG50vp0OyRvqZuzSJfW9y0dX1S3KBMo8k7FrF88Cz4kXE4ZSUbWBmVp4mn306c8dhv6wyvCnEDLzyKaUbRXJ2Q1ErrxKdg4RJ/lykh5Rs+Gdpvu2aq3VpGiMhbyRhXPuPG0O6L7TNvWcrxRX/r8TNYLsrrmHr35dsyghw50aPaxAb7iPtQOIJpvw9OBR/5h7twy0ncuPijvPzOav+Zs277Z65Q0pLWJK/axKQM+qlA5BTSuBZlB+9NYpKPxnSVKfEbuksfklVW7f5Hu9PWbI11a4fVruf6UZEBc14lrRHtG3vfLp0UOUoKZ85N1ijqbR4n8QjiiBeW4PrU4S72M6F2amHLLMcWzKe01bm9Ue9tnR4ufaE57Qr9VgXfFGdnHiKxfBN4pozUZ0a/9Vo5+t0Lag5QspI/VScrYxhXpJOwaS2iXyzUi3xcy6y0mSzYl/pquvbsKWosyzpdeYL6wtrVOWhQJxsQ1V7bd7O1m34NI8yaEvUokRbNWLhH/y/RX/+p1srq0IlDDOAOFsnSu+cgo00AddcnHN9sg3deW8t1ShqdKauP9jEzvViTbpDwJ5UFfPQDOfXqWvHCV5CR3sdRHetGmk1akPF7QI44WvWtHWf2h8r8o9xXykau05zrCvGGjY3/dlzvhXeTbzKtK3Y928X+hbnRd1RpSjIQ5XZUa4s7eY8qxbClTeidJvn0TK0rLWs8XejXzGdFaPLb28p+h9RfwV8utn/3o9CpW4RatAUnBPBmNyJZoqYcfr1sVXnplalrm2fAza1L3slveJCuW1s1kxifBVPZo1bxUZw267jP+A7rDMxrQ7dqKPFuIoA/UnZ8v9TDa/pSnLGU+dtKoxENKO+fxozpgqfK5uEa9YmmtsbTwbTz7RN3enbbvvE2xQ58iHJkdDGgXJBTT6NbmPEhSQF7Xlf2yd1eHWnAv9chCIeXqW4V4dtcX8h1SKeOvlOfIyI6aHaff2TlVfbQN61D9N0vIY8pmC9o7GnGdesRKfluOaGHHX7V8ekRn3l2KWaRfb85I7d5mFqKKvzbZnNwLhlcq3lPR+IjmYCJeN3LbWcoPd6wMMRLyvi8tI3ic5ddBs4x5m1wZOld3R28FzRJ6kpzyeRk19shGLZ8yyFusEWhfr7urJPVM/MHDOsi80uwUe33hZ1OVleDY3oeeqHkz864ePL/UmyPH703us7rkOY5VHDhbeH4zWl3lSarPTXqYLvA1+piKkcoJdfRuMqkqpiM+8uYiJQrjIjE+XMJGESJ/mOQhMst7G1/KuremXM3mpY05opyEew8SEa4I6pIzYrrMjKO3RK9HWJuabOEo4XlXpnJw29riyc+5JV8kW881eqTU8kZ13kJTtz2GseHSQsZk/VLBnYvI3n0h30ety6Ds3OAjKPg3Eq78SXsTn9O1fYgi8b16v29FNN/kv1B1eeIXUQvu5MFCdtpV46z2aJ7lFxZ1m74PB38eCeiakz4hPxgqu6TMS25T96d/Sns4FzErvekZPgabCz+SZU4h40nILvGjSYT+HlPoWDQHn5FUufjzkef+3CgOhf4+XdgYNHV+BFUOITz0/bzfnJve4bxsTs36Wubiy0PacH0joXF4M1afbZh+PhYqt2bk6+eA1uGwgbr2Fv/rODQfwymcly+3gr7r9KXHrMt+sTqzxGg2fM8Ybj6ruZ6jP8+sHJ2Jddz8ZNQWBc1UZo3m66eP0aRZA5rXTMiTQl46ibdXkZHXlwqenLtkyMS/vWSQ+DoZfKnoE/x6SroHT01/0881Kv2Zj0yGTp1MVWpIT2baHdrDMZ0WmJudAT2Xb1s+O796bfFb58uV9vrV31+99uD66se31BfS3xE/E7+EQP6a+FB8LO5AgNkGEU7FX8Rfxd/++J8bF2/8+sYHsuvbbynMT0Xl58Zv/wsjoSbD</latexit> Observations: def. = 1 n Pn i=1 xi <latexit 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<latexit 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Density fitting: Maximum likelihood (MLE) d↵✓(x) = ⇢✓(x)dx <latexit 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g✓ X Z ⇣ Generative model fit: ! MLE undefined. ! Need a weaker metric. ↵✓ = g✓,]⇣ <latexit sha1_base64="W/xAH4ZEbKVL5sYCOuVPDm3rS+Q=">AAA9vXictVttcxu3EYbTl8Tum9N+7EznWsWdJKNqJMWZtpPRjC3JL4oVWzYp24lpa47kiaJ94tF3pGSb4f/pv+g/6Ne2/6D91L/Q3QVwwJG4W0B1dSMJB+J5drEHLHaBY3ecDovJ+vo/L33wgx/+6McffnT5yk9++rOf/+Lqx798XGTTvJcc9rI0y5924yJJh6PkcDKcpMnTcZ7Ep900edJ9tYOfPzlL8mKYjdqTt+Pk+Wk8GA2Ph714AlVHV7dnHSKZ5Ul/3onTo87kZB5tRYOjGZRWO8VJnI/nkWr1LB90n8/WvlxdX137ct55l0zieXR0dWV9bZ1+ouXChiqsCPVzkH38m03REX2RiZ6YilORiJGYQDkVsSjgeiY2xLoYQ91zMYO6HEpD+jwRc3EFsFNolUCLGGpfwd8B3D1TtSO4R86C0D2QksJvDshIXANMBu1yKKO0iD6fEjPW1nHPiBN1ewv/u4rrFGon4gRqOZxu6YvDvkzEsfgT9WEIfRpTDfaup1imZBXUPLJ6NQGGMdRhuQ+f51DuEVLbOSJMQX1H28b0+b+oJdbifU+1nYp/k5bX4IpES/U+KxlicUb8ET3NKXwm9UlB8gAYEtVHLJ2TrU+p9yNoP4P6+3DNqaRt0oVrRrXzRuQOXC7kDou8A5cLeYdF7sPlQu6zyAO4XMgDhURsTjZ341twufAtVvJDuFzIhyzyEVwu5CMW+RguF/Ixi/wOLhfyOxZ5Gy4X8jaLvAeXC3mPRbbhciHbLPIQLhfykEXegsuFvKWQ9TM1hysjniEzK29CuSoDPUUKNTdZ/bbJO7qw2x5zuleD5Wf1Lvx3Y3c9bJrUYG95jLvjGiw/8u6Aj3RjeV90l1YTF/Yui92DEeDG7rHYr8XLGuzXHjPtVQ2Wn2v70M6N5b3vN3Dnxn7DYu9DyY3l16gHUOPGPvBYMcY12AMW+1C8rsH6eP28Bsv7/Rb4FTeWX6fa0N6N9fGm0xos708fQwTjxvKr1ROodWOfsNin4k0N9imL/Ra8uxv7rccK+64Gq9fYK7SCDCgeSWDGNrHF5azE0hjYYkZ+Wq4tKcXGXajnMIMSMyDMKYu4UyLueCL2S8S+t15F6UcLind5Ka0S0fJEdMu1CUsTtn2/bI+l1AOxWyJ2FxBNESk+a92XM4oudA2HnJQrF5Z8+pSV/htLiRoPzZ5XIx5UEHJsn9DIX6VsCTMotFQT20m5xktkRPdNiHPK3nQvtQweNym9go16w6K6DlSXRb11oN6yqKkDNWVRZw7UGYsyM9/GdTxGgLE/PosZ3ckRIGPk+iuCqOAmrDp3YY5GMH4OIAp8RDUP4H+Lcm/uatIMs3lcJ3GX43nFE+dQmokVqDdZ4S7l1ynNsAQ0ky0fqBwf73BvY6bmnPTC83Ilj8odE3+eIekzKHkwWoxoPoXx3KOaOUV3shSGv1vOe10Kw98ii88pipelMPxEaT+5gO5thW1fANuC2TRW1jflUA65/yI5dPkKrbrocfGpnqoxg3xvAvn31JPZu8Bz2aGStI8ph3EUVv+KSv9COIydC8vOYSwYPcmoV5ei4J6MVN5ryqE6ZLSKjpQe5i70yWCbvnoyuhzGcQAR1w7l3DOrHDp6x2VvTDmM47GQ+55ziuR1OYxjQPfSHqYcxoG7LbHK80051LOjBWTubMqhXn1Eu8C4ByTHvKwxUVFOcdJUsQ0pPmjerbFj/uV1DPdsXpQ5QjOTiW3rebrlWtaskY4XEvBqk0A9ML6YWjFYlWMmNtn8SuowqazvyzxmjUfL74MVI5j98gyA2zNPQUO9J4HeOwXGDTbrqvZM4zZZHI6S4wVUR9VO2GjRyJW7RtW6I6rl8jLTW2PHDvnrgsbemGLCfbIsZ4f92idcx8hZaL9iIZ4vxHbv1HytWn+dxY0XEONypPXoREiepDXnqS6rtywbX1OnPBO45JmPGb+423ysvA3mPBn5ItSlSabdTu8j2XW4rq4Ks8ctP4voiaK/OiOvMaQTqYLNQvVusYzGZ3RvuA/pTA5lSI4ePMdIsYyFPDXDXXTcT4/Io9r+lpON9tI7dLJckNfV/rgZPbDQAwc6PMfZgRXjPpTakDMcwl3bI8u5UtoqI4vn4g/l6WhGT7A5o08rHlJzSH+TVDxkU5Z9UmE5BzSOBpml+3Ms8mh8Z4mJz/pd+pjcter5r9HJrT7fjmmM14/m+p2YPkndJKkRzRp5qivvFiVIDWbOTzYpfm3uJcoLkYg+lJP6wpIs7TKiE/+EMtgxRcYpzTZudlRb2/tTi59oSQdCn53jaXZGHjIi/xfB+pTRmIzo1353QJ+gS4+Qko/08TvDMrpxxTpDdoyZOG4o5FsNZrwl5MumJF/z2rOroLEoMwa5DswXxra2yT7FgglJzZV3N3O7efVBpHlPwh4lktGMlU9J/mf0V//qcbKyNCLQwvgECuXrXM8jo5wFbRTTKt/sg3RbW8tPSh1eKK3N+md0+qSi2S5lXKgPrtZ9kNyjeykLR0lOehdLbeQ62rSbi8zjBTtib48pi5d+f6BWYNR7lVbJFZpzHRolAxgFkzKL0G25XeRFuc2yqux+3MX/hd3Yumo1ZIyE2cGVFuL29xPK1mwtUxjVcvy+otnktnq+0KpZzojG4qk1l7+H2t/CX623vvfj6Va8wjaNAclg7oxFZE201MJP1nZFlh6ZmsvcG3lmTOpWds1F8mvp3UyOfRbMckCj5o3atdDli3C8tDheetqwTWeNxoq6XnuiIza3aKvTSl95IdLaAcxTlpmPyDRq6KGlnUv5sfZZVj7H16h3LNc6yxXDbLVPA+w574N0z/XF2f19ubpH4jbFNj2KwGT+0qdZOqSYS9c2Z2qSASVfV/7Vnv0dqkHpXfKgyCzf48QZI0+denTNS01/r1a2jPy88Qj6vaVz1Ub72A6Vv1hCntKcKGheasR1apEo/W09ogWPtGbFHBHt/McUU8m4ozlntlubZxJV4gmTb8pZZWTJTGFE9ud23vaWstc9K3+NKCecqui6C1zhTxgZJEbvJLgjy4KeEK5y8iRBRrRd8p/Lfkqe4o0sjdZI65nY8vAxMus1Y90eW7rHum+fQ0u0unnqrha8vNRbIifvIid6Ma1qpypGnS3cX4wrVqtc9b7JDtMFucYeU2pjZxYmy6tiOuIrbylSozApEuMjJawXIfqHaR6iszyd8mXWrTVzdadB+pgType490AR4YruPnVGc58x/egu8XUJa7PJGo4Jd+MytT9ge1rclbq8tA7J2suNq1FqrUR1K4Vmt1cL47+lh0zI+6WC27ORrW3dO5Ushd+FkQw9Id/orcsPbc6v4MK/kXBlh1qiz95hC+Lbm2JH3HoPb0O8VmW5oxlRDfqC/kLuHat+Vls02+i1xW7z+0jwlzEEW3PaD2klDdVdMvOa2+z+/OfkBXKRsNqbluF9sKXwPVmWFNKfIXk2vjdDob+LE9oXLcGnJ1Up/nLkuQbXi2Ohv9MU1gfNzvegKiFEhn6Pwe+Zm9bhsmxJzfZaluIrQ64C+sRF4/Dkrz5XMe18PFRuPZH3LwG9w3EDu14t/td+aDlGUrgsX2kFfdfspcdTl+0StSOL8XD4nDHSfEZzvUR/mVnZOxMtueXJuC8KelKZ1Zv3z4/xqBkDWtZMyH1QXjuJt0eR0deXBc8FXDpk4j/ir5f4byO8Ljnq9Ahh0ucU9Wy6Bc+mv3Hp6p3+zEcnw1OnU5XN5BEteiN2R+yJ2/C7U0aAoW+Hyu9Syv+IdX9/tg+1x+Q99C663DnoUF1Cux/mFK1P92qP8ejqysbit5CXC4eba39e23h4feXGtvqC8kfi1+J3kJZsiD+KG+IudPcQVPqL+Jv4u/jH1o2t4610aySbfnBJYX4lKj9b5/8FoXTumg==</latexit> <latexit 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<latexit 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<latexit 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↵✓ <latexit 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min ✓ Wp ",p (↵✓, ) <latexit 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  87. Deep Discriminative vs Generative Models ✓1 ✓2 ⇢ ⇢ z

    x g✓ ⇢ ⇢ z x Discriminative Generative d⇠ ⇠1 ⇠2 g✓(z) = ⇢(✓K(. . . ⇢(✓2(⇢(✓1(z) . . .) Deep networks: d⇠(x) = ⇢(⇠K(. . . ⇢(⇠2(⇢(⇠1(x) . . .)
  88. Deep Discriminative vs Generative Models ✓1 ✓2 ⇢ ⇢ z

    x g✓ ⇢ ⇢ z x Discriminative Generative z1 z2 g✓ Z x z X d⇠ d⇠ ⇠1 ⇠2 g✓(z) = ⇢(✓K(. . . ⇢(✓2(⇢(✓1(z) . . .) Deep networks: d⇠(x) = ⇢(⇠K(. . . ⇢(⇠2(⇢(⇠1(x) . . .)
  89. Training Architecture g✓ Z X y1 <latexit 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<latexit 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Stochastic gradient descent <latexit 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<latexit 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↵✓ <latexit 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<latexit sha1_base64="ZvDledmv+Gwz+FxUnlfvrUdxKFc=">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</latexit> min ✓ E(✓) def. = Wp ",p (↵✓, ) <latexit 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<latexit 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✓ ✓ ⌧r ˆ E(✓) <latexit 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<latexit sha1_base64="IBy1TwC0khpcsDQ0WUEsOM5LJ+0=">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</latexit> ˆ E(✓) def. = Wp ",p ( 1 m P i g✓(zi) , ) <latexit 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<latexit 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  90. Training Architecture g✓ Z X y1 <latexit 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<latexit 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Stochastic gradient descent <latexit 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<latexit 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↵✓ <latexit 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<latexit sha1_base64="ZvDledmv+Gwz+FxUnlfvrUdxKFc=">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</latexit> min ✓ E(✓) def. = Wp ",p (↵✓, ) <latexit 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<latexit 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✓ ✓ ⌧r ˆ E(✓) <latexit 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C K . . . ✓1 ✓2 . . . 1m 1/· ⇥mK> ⇥nK 1/· . . . . . . e C/" Input data <latexit 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<latexit 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<latexit 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<latexit 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(y1, . . . , yn) <latexit 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sha1_base64="Lz1gCqAeSuy9yYYGVdEU4UDCj/g=">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</latexit> Generative model <latexit 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<latexit 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<latexit 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(x1, . . . , xm) <latexit 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Sinkhorn, ` = 0, . . . , L 1 <latexit 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ˆ E(✓) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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h(C K)b, ai <latexit 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<latexit sha1_base64="JdisBtcz53UgAh2eCi1NPNdGUeA=">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</latexit> ˆ E(✓) def. = Wp ",p ( 1 m P i g✓(zi) , ) <latexit 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<latexit 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  91. Examples of Images Generation (a) WGAN MNIST (b) WGAN CelebA

    (c) WGAN L (d) MMD GAN MNIST (e) MMD GAN CelebA (f) MMD GAN Figure 2: Generated samples from WGAN and MMD GAN on MNIST, CelebA, and datasets. ⇣ Inputs <latexit 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<latexit 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Generated ↵✓ <latexit 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  92. Examples of Images Generation (a) WGAN MNIST (b) WGAN CelebA

    (c) WGAN L (d) MMD GAN MNIST (e) MMD GAN CelebA (f) MMD GAN Figure 2: Generated samples from WGAN and MMD GAN on MNIST, CelebA, and datasets. ⇣ (a) WGAN MNIST (b) WGAN CelebA (c) WGAN LSUN (d) MMD GAN MNIST (e) MMD GAN CelebA (f) MMD GAN LSUN Figure 2: Generated samples from WGAN and MMD GAN on MNIST, CelebA, and LSUN bedroom datasets. Inputs <latexit 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Generated ↵✓ <latexit 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<latexit 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h⇠ <latexit 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<latexit 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<latexit 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! Performance evaluation of generative models is an open problem. ! Influence of "? <latexit 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<latexit 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<latexit 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! Need to learn the metric d(x, y) = ||h⇠(x) h⇠(y)|| (GANs) <latexit 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<latexit 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<latexit 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Ian Goodfellow " <latexit 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<latexit 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Inception score <latexit 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  93. Progressive Growing of GANs for Improved Quality, Stability, and Variation

    Tero Karras, Timo Aila, Samuli Laine, Jaakko Lehtinen, ICLR 2018 X “fake” <latexit 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<latexit 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g✓
  94. Progressive Growing of GANs for Improved Quality, Stability, and Variation

    Tero Karras, Timo Aila, Samuli Laine, Jaakko Lehtinen, ICLR 2018 X “fake” <latexit 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<latexit 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g✓
  95. A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction:

    O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵
  96. A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction:

    O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)).
  97. A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction:

    O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)). p = 1 d = || · || ! min-cost flow, on graphs O(n2 log(n)). W1(↵, ) = min div(u)=↵ R ||u(x)||dx <latexit 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<latexit 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  98. Monge-Amp` ere/Benamou-Brenier, d = || · ||2 2 . A

    Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction: O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)). p = 1 d = || · || ! min-cost flow, on graphs O(n2 log(n)). W1(↵, ) = min div(u)=↵ R ||u(x)||dx <latexit 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  99. Monge-Amp` ere/Benamou-Brenier, d = || · ||2 2 . Semi-discrete:

    Laguerre cells, d = || · ||2 2 . A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction: O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)). p = 1 d = || · || ! min-cost flow, on graphs O(n2 log(n)). W1(↵, ) = min div(u)=↵ R ||u(x)||dx <latexit 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  100. Monge-Amp` ere/Benamou-Brenier, d = || · ||2 2 . Semi-discrete:

    Laguerre cells, d = || · ||2 2 . A Glimpse at Algorithms Linear programming: O(n 3 log(n)2) Hungarian/Auction: O(n 3) = 1 n Pn j=1 yj ↵ = 1 n Pn i=1 xi ↵ ↵ ↵ 1-D case: sorting O(n log(n)). p = 1 d = || · || ! min-cost flow, on graphs O(n2 log(n)). W1(↵, ) = min div(u)=↵ R ||u(x)||dx <latexit 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Entropic regularization: generic d. <latexit 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<latexit 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