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10-ot-generic-bio.pdf

 10-ot-generic-bio.pdf

Gabriel Peyré

January 14, 2024
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  1. Gabriel Peyré É C O L E N O R

    M A L E S U P É R I E U R E Optimal Transport for Machine Learning and Genomics Geert-Jan Huizing Laura Cantini
  2. Comparing Distributions for Learning <latexit sha1_base64="vT0xGll5ZYO8gmdwavYy0Ckm65g=">AABB13ictVzbchu5EYU3t7Vz8yaVp7xMonXKu+V1JK0rm62tVK0sybLWtC2blGzv0nbxMqJpDzk0h5QvXFXeUnnNJ+Q1+Yh8R/4gecovpC/AAENipjGKY5QkDIjT3egBGt0N0N1JMsxm6+v/PPfed777ve//4P3zF374ox//5KcXP/jZUZbOp734sJcm6fRht5PFyXAcH86GsyR+OJnGnVE3iR90X2zj5w9O4mk2TMet2ZtJ/HjUGYyHx8NeZwZNTy/+ok00Ft1kHp9GW62t7U+y+OXTi2vrV9fpX7Ra2dCVNaX/HaQfRIeqrfoqVT01VyMVq7GaQT1RHZVB+UZtqHU1gbbHagFtU6gN6fNYnaoLgJ1Drxh6dKD1BfwewNM3unUMz0gzI3QPuCTwMwVkpC4BJoV+U6gjt4g+nxNlbC2jvSCaKNsb+NvVtEbQOlPPoFXCmZ6hOBzLTB2r39MYhjCmCbXg6Hqaypy0gpJHzqhmQGECbVjvw+dTqPcIafQcESajsaNuO/T5v6gntuJzT/edq3+TlJegRKqpR5/mFDrqhOhH9Dbn8BnLkwDnAVCI9Rix9op0PaLRj6H/AtrvQDmlmtFJF8qCWk8rkdtQfMhtEbkHxYfcE5ENKD5kQ0QeQPEhDzQSsVPSuR/fhOLDN0XO96D4kPdE5H0oPuR9EXkExYc8EpFfQ/EhvxaRN6D4kDdE5C0oPuQtEdmC4kO2ROQhFB/yUETuQvEhdzWyfKVOoaREZyisyi2oF3mgpUigZUuU7zpZRx/2esCa7pVg5VW9A3/92J0AncYl2N2AeXdcgpVn3h7YSD9WtkU3aTfxYW+K2H2YAX7svoj9Sj0vwX4VsNJelGDltdaAfn6sbH1vw5Mfe1vE3oGaHyvvUXehxY+9G7BjTEqwByL2nnpZgg2x+tMSrGz3m2BX/Fh5n2pBfz82xJrOS7CyPT0CD8aPlXerB9Dqxz4QsQ/V6xLsQxH7CKy7H/soYId9W4I1e+wF2kEG5I/EsGKrqHXyVYm1CVDrCPyTfG9JyDfuQruEGeSYAWFGImIvR+wFIho5ohEsV5bb0Yz8XZlLM0c0AxHdfG/C2kzs38/7Yy0JQOzkiJ0lRJVHiu/ajOWEvAvTIiFn+c6FtZAxpbn9xlqs50O15TWIuwUEz+1nNPOvULSEERRqqoras3yPZ2REz1WIVxS9mVEaHjJullsFF/VaRHU9qK6IeuNBvRFRcw9qLqJOPKgTEWVXvotrB8wAq398Fwt64hnAPnJ5icAr2IJd5yas0QjmzwF4gfep5S78bVLsLZUqyTCax30SsxyPC5Z4CrWFWoN2GxXuUHyd0AqLQTLueVfH+PiEuY2FXnNshU/znTzKMybhdIYkzyCng95iROupHp1b1HJK3h3X6uFv5uve1Orhd0njp+TFc60efqaln51B9pbGts6AbcJqmmjt23pdGpx/YRqmfoF2XbS4+FZHes4gvdc16e/rN7N/hveyTTXWj63Xo5E548sK46tDw+o5c/Rcjwp6T+z1mlpUeyRjHffael0ZUtpFx1oO+1T3zWCfvn4zpl6PxgF4XNsUcy+cet3ZO8lHY+v1aBwpznuekidv6vVoDOiZ9WHr9WhgtqWj43xbr2vZUQMcO9t6Xas+piww5oB4znOL9Yqm5CfNNbUh+QfV2RrX51/dxzBn8ySPEaopWd+2nE4338uqJTL+QgxWbVZTDvQv5o4PVqSxUJtifMUyzAr7+yodu8ej5hugxQhWP58BSDnzBCQ0OQm03glQ3BCjruLIDG5TxOEsOV5CtXXrTPQWLV/OGhXbnlKrFJfZ0Vo9tsleZzT3JuQTNkizkh4apW+4jKKkoUZBQzK9Orp7q9drUfvrIm6yhJjkM61HJ0J8klYdp/q03nR0fEmf8syg8JmPnb+YbT7W1gZjnpRsEcpSxdPtZ/JIbhvuq1eUzXHzZxG9UbRXJ2Q1hnQilYlRqMkWsze+oGdL+5DO5JAH0+jBe4w0lYniUzPMomM+PSKL6tpbiTfqy2TouJ6R1TX2uBo9cNADD7p+jLMNO8YdqLUgZjiEp1ZAlHMh11VKGp+qT/LT0ZTeYHVEnxQspKHB9iYuWMiqKPtZgcorQONs4Cg9nMYyHYNvr1CSo36fPDZ2LVr+S3Rya863OzTHy2dzeSamT1w3iWtEq4ZPdflpmQNLsPB+skn+a/UokV8djmhDJa5PHM6slzGd+McUwU7IM05otUmro9jbzU8tf2I4HShzdo6n2SlZyIjsXwT7U0pzMqIf9+6AOUFni5CQjQyxO8Pcu/H5OkNxjlk/bqj4VoOdbzHZsjnxN3Td1ZXRXOSIgfeB06W5bXTSIF8wJq5Tbd3t2q7efRBp70m4s4Qp2rlymfh/RL/Nj5knayszAjWMbyDTts73PlKKWVBHHdrlq22Q6etK+WEuwxMttd3/rEwfFiTboYgL5cHdug+ce/TMvHCWTEnubKUP76NV2VykPFnSI472mKJ4tvsDvQOj3Fdol1yjNdemWTKAWTDLowjTV8oiL/Ot5lWkHkY7+79Qt7ouag0pRspmcFlDUn4/pmjNlTKBWc3z9wWtJr/Wp0u9qvmMaS6OnLX8LbT+Cn4buc1zGJ1uwSpcpznAFOyT1Qi3RCs9wnhdL/AyM9PQss+Wn52Tppfbcpb4mq2bjbFPalM5oFnzWmctTP0sNJ47NJ4H6rBFZ41Wi6bdWKKnYmzR0qeVofzqcGvVoDwXKcsemUENA6R0Y6kwqn2RqhzjG9Rbkda6SKsDq9U9DXDXfAjSv9aXV/e3+e4eqRvk2/TIA+P4pU+rdEg+l2mtjtSYAnK+pu2ru/rb1ILcu2RBkTLf48QVw6dOPSqnuaS/0TtbSnbeWgRzb+mV7mNsbJvqn64gR7QmMlqXBnGNesRafleOaMkiXXV8jogy/x3yqdjvqI6Z3d72nUQFf8LGm7yqLC+OFMakfynztr8Sve478WtEMeFce9ddoFX/DSMFxphMgt+zzOgN4S7HJwns0XbJfq7aKT7FGzsSXSWpF+oPATaGo1471925ZUZsxvYx9ESt27fu6yHzS4I5SvzOcqLXoV1tpH3UxdLz2Wh19C5XfK7Sw3yJr9XHnPq4kYWN8oqYtvoimAtLVI8LY0K41BtFHfnrSV5HZj6dCqVsehvKxUwD25hnFC9J90AR4fPuLnu9uY+EcXRX6HUJ61LjFokSZuNSnR9wLS1mpc6v7EPcer5yN0qcnahspzDU3d3C2m+2kDFZv0RJORvu7creLkQpchaGKfQU3+gtiw9dml9Awd+R8kWHhmNI7rAJ/u2W2la77+A2xEtd54xmRC1oC/pLsXdHj7PYo1pHLx3qLv0QDuE8hqBrSfoh7aR1ZWfKsuQu9XD6r8gKTFUsSm971h+Dy0UeySqnOuMZkmWTRzNU5rs4dcdiOISMpMglnA+fa0ijOFbmO031xmCoyyMocqjDw9xjCHvntnd9Xi6nan2tcgnlwbuAOXExODz5K49VbL8QCzV13si754DW4biCutkt/tdxGD6WU31eodwy+q7Z84C3zv1inZFFf7j+mrHcQmZzOcdwnmk+Oust+fmx3xfVelOpM5p3Tx/9UTsHDK+F4jyoLB3j3Vlk5Q2lgucCPhlS9R/1j3PytxFe5jTK5KhDyZxTlFMzPWRq5huXvtGZz0JksnTKZCpSs3FEk27Ebqt9dQN+tnMPsO7tUP4uJf9FrP/7s31oPSbrYbLonDloU1tM2Q97itanZ3t/tkxivMvLd3tb0IJn4Q1qxXu+d6g/3vVtFcZW/g0SXuu3Var6hYhk+XTPrqsujKB48sY5IPM934ju0nMWi2+ejQLOFs39qWWJFvSJfLOgW4rvOlL2aK5O9Fk9nhzgDftOnh+K1G+praPtPO65EueDUs4HS5wz0k6Rw2vns+q7WWVcth0u/Tx3dqL7pRRn2/O86tzoTikXvoNejR9U4AeOlE3S/guKhKeqOps3r6A51zK5J6xjZTKRrAeMMzv5+66ObE8qeJ0EjP9WKfqWI+keyNKl/HdEJ2xTopdo3eyS9HzTsTqTerNCWv09SvrfDT6nfxFXPrumK59v5P+7wdHm1Y3fXf303ubal9f1/3Pwvvql+rW6DGv8M/UlUDtQh3Tq/Vf1N/X3rUdbf9z609afuet75zTm56rwb+sv/wUQUKl9</latexit> ATAC-seq

  3. Comparing Distributions for Learning 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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<latexit 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↵✓ <latexit 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ATAC-seq
  4. Comparing Distributions for Learning min ✓ D(↵✓, ) <latexit sha1_base64="9IYkKnkiR+VYnIAjCg9CiCnhkKw=">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</latexit>

    <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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<latexit 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↵✓ <latexit 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ATAC-seq
  5. x <latexit 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<latexit 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<latexit 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<latexit

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d(x,y) <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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2. Entropic <latexit 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<latexit 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Regularization <latexit 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1. Optimal Transport <latexit 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<latexit 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4. Gromov Wasserstein <latexit sha1_base64="9fqK2kknFwBXfI8mtR1BkfiXw2M=">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</latexit> 3. Single cell genomics
  6. Monge’s Problem Monge optimal matching: <latexit sha1_base64="cXrrsZJZuxRia1oYbgE1ijicFzU=">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</latexit> <latexit sha1_base64="cXrrsZJZuxRia1oYbgE1ijicFzU=">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</latexit> <latexit

    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<latexit 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[Monge 1784] <latexit 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<latexit sha1_base64="UVBrgZLymtr0d1RvatLpsl9X7ek=">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</latexit> 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 sha1_base64="htpgxAyMB7fa8Ak1IhsYtBIZXuE=">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</latexit> D(X, Y ) = min n X i=1 d(xi, y (i) )
  7. Monge’s Problem Monge optimal matching: <latexit sha1_base64="cXrrsZJZuxRia1oYbgE1ijicFzU=">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</latexit> <latexit sha1_base64="cXrrsZJZuxRia1oYbgE1ijicFzU=">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</latexit> <latexit

    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<latexit 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[Monge 1784] <latexit 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<latexit sha1_base64="UVBrgZLymtr0d1RvatLpsl9X7ek=">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</latexit> 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 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! Di↵erent number of points?
  8. 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>
  9. 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>
  10. 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
  11. Optimal Transport Distances Wp(↵, ) def. = <latexit sha1_base64="ZLn74A+pY2ZqHm9oqSjbdpXOK7s=">AABFHXictVxfbxu5EWeu/67uv1z72Je9OimSwk1t94oWCApcYjmOL0riRLKTuygxdqWVomStVbSS4kSnz1L0k/Sp6EtRtE9FP0CB9qlfoTNDcsmVuDtc95qFbS6Xv5nhLDmcGXITjZNhNt3e/selD7729W9881sffnvjO9/93vd/cPmjH55k6WzSjY+7aZJOnkZhFifDUXw8HU6T+Ol4EodnURI/iV7v4fMn83iSDdNRe/puHD8/CwejYX/YDadQdXr55pXOND6fLp4sTxfj5bVFh0guJnFv2QmT5ZauiJJZvOxE8fJ60Inf9OJ+cGXj9PLm9o1t+hesF3ZUYVOof0fpRx//U3RET6SiK2biTMRiJKZQTkQoMrieiR2xLcZQ91wsoG4CpSE9j8VSbAB2Bq1iaBFC7Wv4PYC7Z6p2BPdIMyN0F7gk8DMBZCCuAiaFdhMoI7eAns+IMtaW0V4QTZTtHfyNFK0zqJ2Kl1DL4XRLXxz2ZSr64jfUhyH0aUw12LuuojIjraDkgdWrKVAYQx2We/B8AuUuIbWeA8Jk1HfUbUjP/0UtsRbvu6rtTPybpLwKVyBaqvdpTiEUc6If0NucwTMpTwKcB0AhVn3E0lvS9Rn1fgTtF1D/AK4llbROIrgWVLusRO7B5ULuscgDuFzIAxbZhMuFbLLII7hcyCOFROyEdO7Gt+By4Vss50dwuZCPWORjuFzIxyzyBC4X8oRFfgGXC/kFi7wDlwt5h0Xeg8uFvMci23C5kG0WeQyXC3nMIvfhciH3FbJ8pk7gSonOkJmVt6Bc5IGWIoGaW6x8t8k6urC3PeZ0twTLz+oG/HVjGx46jUuw+x7jrl+C5UfeAdhIN5a3RXdpNXFh77LYQxgBbuwhi/1MvCrBfuYx016XYPm51oR2bixvfe/DnRt7n8U+gJIby69RD6HGjX3osWKMS7BHLPaReFOC9bH6kxIsb/dbYFfcWH6dakN7N9bHms5KsLw9PQEPxo3lV6snUOvGPmGxT8V5CfYpi/0crLsb+7nHCvu+BKvX2A1aQQbkj8QwY6uohfmsxNIYqIUM/yRfWxLyjSOo5zCDHDMgzBmLOMgRB56IZo5oesuV5XY0I3+X59LKES1PRJSvTViasu17eXssJR6IRo5orCCqPFJ817ovc/IudA2HnOYrF5Z8+pTm9htLsRoP1ZZXIx4WEHJsv6SRv0XREkZQqKkqai/zNV4iA7qvQryl6E33UvPgcdPcKtiocxYVOVARi3rnQL1jUTMHasai5g7UnEWZmW/jOh4jwOgf38WC7uQIkD5y+RWAV3ALVp27MEcDGD9H4AU+ppqH8LdFsTd3VUmG0Tyuk5jleF6wxBMoLcQm1JuosEHxdUIzLAbJZMuHKsbHO8xtLNSck1Z4ma/kQZ4x8aczJHkGOR30FgOaT/Xo3KOaJXl3slQPfzef97pUD79PGl+SFy9L9fBTJf30ArK3FbZ9AWwLZtNYad+U69KQ+RdJQ5c3aNVFi4tv9UyNGaR3XpP+oXozhxd4L3tUkvox5Xo0Mqt/WaF/dWgYPWeWnutRQe9Jer26FNTuyUjFvaZcV4aUVtGRksPc1X0z2Kan3owu16NxBB7XHsXcC6tcd/SO896Ycj0aJ0LmPZfkyetyPRoDupf6MOV6NDDbEqo435TrWnbUgIydTbmuVR9RFhhzQHLMyxrjFU3IT5opakPyD6qzNbbPv76OYc7mRR4jVFMyvm05nShfy6ol0v5CDFZtWlMO9C9mlg9WpLEQu2x8JWWYFtb3dTpmjUfNN0GLAcx+uQfA5cwTkFDnJNB6J0Bxh426ij3TuF0Wh6Okv4LqqNop6y0avjJrVKw7pVouLjO9NXrskL3OaOyNySdskmY5PTRL33AZRU5DzYKGeHp1dPdezdei9rdZ3HgFMc5HWpd2hOROWnWc6tJ6y9LxVbXLM4VL7vmY8YvZ5r6yNhjzpGSLUJYqnnY7nUey63Bd3RImxy2fBfRG0V7NyWoMaUcqY6NQnS2W3viC7g3tY9qTQx6SRhfeY6CojIXcNcMsOubTA7Kotr3leKO+dIZOljOyutoeV6MHFnrgQNePcfZgxXgApTbEDMdw1/aIcjZyXaWk8Yn4eb47mtIbrI7ok4KF1DSkvYkLFrIqyn5ZoPIW0DgaZJTuT2OVjsZ31ijxUb9LHhO7Fi3/Vdq51fvbIY3x8tFcnonpEddd4hrQrJG7uvJulYOUYOF8skv+a3UvkV8djmhDOa4vLM5SLyPa8Y8pgh2TZ5zQbONmR7G1nZ9afaI5HQm9d4672SlZyIDsXwDrU0pjMqAf++yA3kGXFiEhG+ljd4a5d+PydYbsGDN+3FDIUw1mvMVky2bEX9O1Z1dGY1FGDHIdWK6Mba2TJvmCMXGdKOtu5nb16oNIc07CHiWSohkr14j/dfqtf/Q42VwbEahhfAOZsnWu95FSzII6CmmVr7ZBuq0t5ZVchhdKarP+GZmuFCRrUMSF8uBq3QPOXbqXvHCUTEjubK2NXEersrlIebyiR+xtn6J4afcHagVGubdoldykOdehUTKAUTDNowjdlssir/Kt5lWk7kc7+79QN7ouag0pBsJkcKWGuPx+TNGaLWUCo1qO39c0m9xan6y0quYzorF4Zs3lL6H2Y/it5db3fnSiglW4TWNAUjB3RiOyJlhr4cfrdoGXHpmalrk3/MyY1K3smovE19K6mRh7XpvKEY2ac5W10OWL0Hhl0XjlqcM27TUaLep6bYlO2diirXYrffnV4dauQXnGUuY9Mo0aekhpx1J+VHssVT7G16j3LK1tllYIs9XeDbDnvA/SPddXZ/eX+eoeiDvk23TJA5PxS49m6ZB8Ll1bHalJCsj5E2Vf7dnfoRrkHpEFRcryHCfOGLnr1KVrmUv6U7WypWTnjUXQ55beqjbaxnao/Ms15BnNiYzmpUZ8Qi1iJb8tR7BikW5YPkdAmf+QfCrpd1THzHZr806Cgj9h4k05qwwvGSmMSP9c5u1wLXo9tOLXgGLCmfKuI6BV/w0jBYnRmQS3Z5nRG8JVTu4kSI82Ivu5bqfkLt7IkugGSb0Qv/WwMTLqNWPdHlu6x7pvP4OWqHXz1l0teH6JN0eO30V29EJa1c6Uj7pYub8YrVCtcsX7Kj3MVvgafcyojR1ZmCiviOmIm95cpET1uEiMD5d6vagjfz3J68gsd6d8KevWmnIx0yBtzEuKl7hzoIhweXfXnN7cdaYf0Rq9iLA2NVnDUcJsXKryA7alxaxUsBIh2fXcmpRY61HZemF42KuGsePSUsZkBRPB5W5ka7sPnUK0wmdjJIWukCd7y+JEm+ZNuPB3IFxRoubok0NsgZ97S+yJ/a/gVMQbVZaZzYBq0Cb0VmLwUPWz2KJaR28s6jZ9Hw7+PIaga076Ia2odWWXlHnJber+9N+SNZiImJXetKzfB5sL35N1TnX6MyQLx/dmKPQ3OXX7ojn49KTIxZ+P3N/getEX+tumen3Q1PkeFDnU4aHPM/i9c9O6Pi+bU7W+1rn48pDrgN550TjcASyPWUw7Hws1sd7IV88BrUO/grpeLf7Xfmg+hlN9Xr7cMvrm7JXHW5ftYpWZRb+4/pwx3HxGczlHf55p3jvjNbn5Sf8vqPWmUqs3Xz199EvNGNC8FkLmQ3npJN4eRUZeXyq4P+CSIRX/EX+4xH+V8CanUSZHHUp6v6Kcmm7BU9NfXrp6p5/5yGTolMlUpGbiiRadjN0Th+IO/OzlHmDdU6Lym0r5F7Hu72h7UNsn66Gz6TKD0KG6mLIgZjetR/fmHG2ZxHimV57xbUMN7ok3qRbP+z6g9njmt13oW/mXJHKu3xep6BUik9VdPjOvIuhBcQdO5oL0974BnamX2Sx5Au3MY49RnqOSkZL++nlBiB7FhauSLgihR0sV5chJOaIzSXEJ7ajQty6N8LHa6cd9BzyfH+bZpUD8gupCtTrgSs1JdeSQ6hllBiLS/zZEaL8SW/B3S5Xdkh6tSZrROyhKdG49qz4JtnSOC/M141XKg+lM3Vy1SymqN7uH1ZnYRikXeeK9Gj+owA8sKVv0tl5T3D0R1bnDWQXNmZLJ3s8dCZ33lHrAaDbMx0d1/Dyv4DX36P+9UvQ9S9IDkCWibHtA+3kTopco3eyT9PJcZXXe9m6FtPqrTUnTnKw040CfkazeE0jUuCuf/fIcJJeriUvo2HNdnsjkTosMnZT4+Tn2OA0RevSW76tPTzkqM1aSmceXyHMPWeYedPqMNH2WwoCVRNmH08ubO6v/18d64WT3xs72jZ1Hu5uf3lb/D8iH4sfiJ+IarH2/Fp/C+D8Sx8Dp9+JP4q/ib43fNf7Y+HPjL7LpB5cU5kei8K/x9/8CVmRYew==</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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  12. Optimal Transport Distances Theorem: <latexit sha1_base64="cHzNFJNn6IKb0rmopfqU8lH/agk=">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</latexit> <latexit 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<latexit 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Wp is a distance and <latexit 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↵n * , Wp(↵n, ) ! 0 <latexit 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sha1_base64="WQok2bKDJeg5qX4mzOisrJyO5D8=">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</latexit> Wp(↵, ) def. = <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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R X fd↵n ! R X fd <latexit 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<latexit 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<latexit 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sha1_base64="U0GVR/6CttHrp/Fuy5L8WQi3+Sg=">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</latexit> Convergence in law: <latexit 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<latexit 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↵n <latexit sha1_base64="4yZ+zpv4dMvD7ccpbygY7mM9Krg=">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</latexit>
  13. Optimal Transport Distances Theorem: <latexit sha1_base64="cHzNFJNn6IKb0rmopfqU8lH/agk=">AABDD3ictVzNchu5EYY3f2vnz06OuUyidcqb8iqS46qkspWqtX4say3bsknJ3l3aLv6MKNpDDs0hJdlcPUQeINfkEXJLcs0j5A2SUw55gfQPMMCQmGmM4nhKEgbE191oAI3uBujOOBlk07W1f1z64Bvf/Na3v/Ph5Svf/d73f/DDq9d+dJils0k3PuimSTp51mlncTIYxQfTwTSJn40ncXvYSeKnndeb+PnTk3iSDdJRc/p2HD8ftvujwdGg255C1cur11rT+Axw8+ZxnE7i4W/PX15dWVtdo3/RcmFdF1aU/refXov+o1qqp1LVVTM1VLEaqSmUE9VWGTxfqXW1psZQ91zNoW4CpQF9HqtzdQWwM2gVQ4s21L6G3314+0rXjuAdaWaE7gKXBH4mgIzUdcCk0G4CZeQW0eczooy1ZbTnRBNlewt/O5rWEGqn6hhqJZxpGYrDvkzVkfoN9WEAfRpTDfauq6nMSCsoeeT0agoUxlCH5R58PoFyl5BGzxFhMuo76rZNn/+TWmItvnd125n6F0l5HZ5INXTv05xCW50Q/YhGcwafsTwJcO4DhVj3EUunpOsh9X4E7edQ/xCecyoZnXTgmVPteSVyEx4fclNE7sDjQ+6IyD14fMg9EbkPjw+5r5GInZDO/fgGPD58Q+T8GB4f8rGIfAKPD/lERB7C40Meisgv4fEhvxSRd+HxIe+KyPvw+JD3RWQTHh+yKSIP4PEhD0TkNjw+5LZGlq/UCTwp0RkIq/IOlIs80FIkUHNHlG+DrKMPuxGwprslWHlVb8FfP3YrQKdxCXY7YN4dlWDlmbcDNtKPlW3RPdpNfNh7InYXZoAfuytiP1evSrCfB6y01yVYea3tQTs/Vra+D+DNj30gYh9CyY+V96hHUOPHPgrYMcYl2H0R+1i9KcGGWP1JCVa2+w2wK36svE81ob0fG2JNZyVY2Z4eggfjx8q71VOo9WOfithn6qwE+0zEfgHW3Y/9ImCHfVeCNXvsFdpB+uSPxLBiq6i181WJpTFQawv8k3xvScg37kC9hOnnmD5hhiJiJ0fsBCL2csResFxZbkcz8ndlLo0c0QhEdPK9CUtTsX0vb4+lJACxlSO2FhBVHimOtenLCXkXpkZCTvOdC0shfUpz+42lWM+HastrEI8KCJ7bxzTzb1K0hBEUaqqK2nG+xzMyovcqxClFb6aXhoeMm+ZWwUWdiaiOB9URUW89qLciauZBzUTUiQd1IqLsyndxrYAZYPWPYzGnN54B7COXPxF4BXdg17kHazSC+bMPXuATqnkEfxsUe0tPlWQYzeM+iVmO5wVLPIHSXK1AvY0Ktyi+TmiFxSAZt3ykY3x8w9zGXK85tsLn+U4e5RmTcDoDkqef00FvMaL1VI/Ofao5J++OS/Xw9/J1b0r18Nuk8XPy4rlUDz/V0k8vIHtTY5sXwDZgNY219m25Lg3OvzANU75Cuy5aXBzVoZ4zSO+sJv1dPTK7FxiXTSqxfmy5Ho3M6V9W6F8dGlbPmaPnelTQe2Kv15Si2j0Z6bjXluvKkNIuOtJy2Le6I4NtenpkTLkejX3wuDYp5p475bqzd5z3xpbr0ThUnPc8J0/elOvR6NM768OW69HAbEtbx/m2XNeyowY4drblulZ9RFlgzAHxnOca6xVNyE+aaWoD8g+qszWuz7+8j2HO5kUeI1RTsr5tOZ1OvpdVS2T8hRis2rSmHOhfzBwfrEhjrm6J8RXLMC3s78t07B6Pmt8DLUaw+vkMQMqZJyChyUmg9U6A4roYdRV7ZnC3RBzOkqMFVEvXTkVv0fLlrFGx7iXVSnGZ7a3VY4vsdUZzb0w+4R5pVtLDXukIl1GUNLRX0JBMr47u3un1WtT+mogbLyDG+Uzr0okQn6RVx6k+rTccHV/XpzxTePjMx85fzDYfaWuDMU9KtghlqeLptjN5JLcO99Wbyua4+bOIRhTt1QlZjQGdSGViFGqyxeyNz+nd0j6gMznkwTS6MI6RpjJWfGqGWXTMp0dkUV17K/FGfZkMHZczsrrGHlej+w6670HXj3E2Ycd4CKUmxAwH8NYMiHKu5LpKSeMT9Ul+OprSCFZH9EnBQhoabG/igoWsirKPC1ROAY2zgaP0cBqLdAy+tURJjvp98tjYtWj5r9PJrTnfbtMcL5/N5ZmYHnG9RVwjWjV8qstvixxYgrn3k1vkv1b3EvnV4Yg2VOL6wuHMehnRiX9MEeyYPOOEVpu0Ooqt3fzU4ieG074yZ+d4mp2ShYzI/kWwP6U0JyP6ce8OmBN0tggJ2cgQuzPIvRufrzMQ55j14waKbzXY+RaTLZsRf0PXXV0ZzUWOGHgfOF+Y20Yne+QLxsR1oq27XdvVuw8i7T0Jd5YwRTtXbhD/j+m3+THzZGVpRqCGcQQybet845FSzII6atMuX22DTFtXyo9yGV5oqe3+Z2X6qCDZFkVcKA/u1j3g3KV35oWzZEJyZ0tteB+tyuYi5fGCHrG3RxTFs93v6x0Y5b5Ju+QKrbkWzZI+zIJpHkWYtlIWeZFvNa8i9TDa2f+FutV1UWtIMVI2g8sakvL7MUVrrpQJzGqev69pNfm1PlloVc1nRHNx6Kzlr6H2p/DbyG3ew+h0ClZhg+YAU7BvViNcEy21COO1UeBlZqahZd8tPzsnTSu35iLxNVs3G2Of1KayT7PmTGctTPkiNF45NF4F6rBJZ41Wi6beWKKXYmzR1KeVofzqcGvWoDwTKcsemUENAqR0Y6kwqj2RqhzjG9Q7kdaaSKsNq9U9DXDXfAjSv9YXV/fX+e4eqbvk23TJA+P4pUerdEA+l6mtjtSYAnK+re2ru/pbVIPcO2RBkTLf48QVw6dOXXrOc0l/rne2lOy8tQjm3tKpbmNsbIvKv1pCDmlNZLQuDeI2tYi1/K4c0YJFWnV8jogy/23yqdjvqI6Z3dZ2TKKCP2HjTV5VlhdHCiPSv5R5212KXned+DWimHCmvesO0Ko/wkiBMSaT4PcsMxoh3OX4JIE92g7Zz2U7xad4I0eiVZJ6rn4XYGM46rVz3Z1bpsemb7+Alqh1O+q+FjK/JJijxO8iJ3pt2tWG2kedL7xfjFZb73LF9yo9zBb4Wn3MqI0bWdgor4hpqU+DubBE9bgwJoRLvV7Ukb+e5HVk5tOpUMqmtaFczDSwjTmmeEm6B4oIn3d3w+vNfSz0o7NEr0NYlxrXSJQwG5fq/IBraTErdXlpH+Lay5W7UeLsRGU7haHu7hbWfrOFjMn6JUrK2XBrV/ZWIUqRszBMoav4Rm9ZfOjS/BQe/B0pX3RoOIbkDhvg395Rm2r7PdyGeKPLnNGMqAZtQW8h9m7rfhZbVOvojUPdpR/CIZzHAHQtST+gnbSu7ExZltylHk7/lKzARMWi9LZl/T64XOSeLHOq058BWTa5NwNlvotTty+GQ0hPilzC+fC5htSLI2W+01SvD4a63IMihzo8zD2GsDG3revzcjlV62uZSygP3gXMiYvB4clfeaxi24VYqIkzIu+fA1qHowrqZrf4X/th+FhO9XmFcsvou2avAkad28U6I4v+cP01Y7mFzOZyjuE807x31lvy82O/L6o1UqnTm/dPH/1ROwcMr7niPKgsHePdWWTlDaWC5wI+GVL1b/XXS/K3Ed7kNMrkqEPJnFOUUzMtZGrmG5e+3pnPQmSydMpkKlKzcUSDbsRuql11F342cw+w7u1Q/i4l/0Ws//uzPag9IuthsuicOWhRXUzZD3uK1qN3e3+2TGK8y8t3e5tQg2fhe1SL93wfUnu869ss9K38GyS81h+oVPUKEcni6Z5dVx3oQfHkjXNA5nu+Ed2l5ywW3zwbBpwtmvtTixLN6RP5ZkGnFN9xpOzSXB3rs3o8OcAb9u08PxSpX1JdW9t53HMlzvulnPcXOGeknSKHM+ez6rtZZVw2HS69PHd2otulFGfb87zq3OhWKRe+g16N71fg+46UDdL+a4qEJ6o6mzeroDnTMrknrCNlMpGsB4wz2/l4V0e2JxW8TgL6f78Ufd+RdAdk6VD+O6ITtgnRS7Rutkl6vulYnUm9VyGt+R4l07R3He08MLcWq7P0iZ53nLkw/xvBnNYD7qbmZqKUPYlL6HToRmBMlPiOZDWlI0GeI5FCX5REz9SXV1fWF/8fiOXC4a3V9bXV9ce3Vz7b0P9HxIfqJ+pn6gbYx1+rz2Ak9tUBcDpVf1B/VH/a+P3Gnzf+svE3bvrBJY35sSr82/j7fwFq0eia</latexit> <latexit 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<latexit 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Wp is a distance and <latexit 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↵n * , Wp(↵n, ) ! 0 <latexit 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sha1_base64="WQok2bKDJeg5qX4mzOisrJyO5D8=">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</latexit> Wp(↵, ) def. = <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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<latexit 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|| xn x ||TV = 2 , <latexit 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<latexit 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<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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sha1_base64="U0GVR/6CttHrp/Fuy5L8WQi3+Sg=">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</latexit> Convergence in law: <latexit 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<latexit 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↵n <latexit 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  14. x <latexit 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<latexit

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d(x,y) <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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2. Entropic <latexit 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<latexit 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Regularization <latexit 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1. Optimal Transport <latexit 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<latexit 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4. Gromov Wasserstein <latexit sha1_base64="9fqK2kknFwBXfI8mtR1BkfiXw2M=">AABB93ictVzNchu5EYY3f2vnz5scc5lE65Q3pVVkrZ2kaitVK0uyrDVtyyYle9e0XRxyRI895NAzpCybyyfJIbdUrnmCVK7JE+QNklNeIf0DDDAkZoBRHKMkYUB83Y0eoNHdAB1Okjifbm7+88IH3/r2d777vQ8vXvr+D374ox9f/ugnx3k6y/rRUT9N0uxx2MujJB5HR9N4mkSPJ1nUG4VJ9Ch8tYOfPzqNsjxOx53p20n0dNQbjuOTuN+bQtPzyze6RONJNgyfzjdurG+ub9xYBN1pdDYNT+afbQTteDxMoqAfJUkwjMbpKO7ni+eX1zY3NulfsFq5JitrQv47TD8KjkRXDEQq+mImRiISYzGFeiJ6IofyRFwTm2ICbU/FHNoyqMX0eSQW4hJgZ9Argh49aH0Fv4fw9ES2juEZaeaE7gOXBH4yQAbiCmBS6JdBHbkF9PmMKGNrFe050UTZ3sLfUNIaQetUvIBWF0719MXhWKbiRPyOxhDDmCbUgqPrSyoz0gpKHhijmgKFCbRhfQCfZ1DvE1LpOSBMTmNH3fbo839RT2zF577sOxP/JimvQAlEW44+LSj0xCnRD+htzuAzlicBzkOgEMkxYu0N6XpEox9D/zm034OyoJrSSQhlTq2LWuQOFBtyx4nch2JD7juRLSg2ZMuJPIRiQx5KJGIz0rkd34Ziw7ednB9AsSEfOJEPodiQD53IYyg25LET+TUUG/JrJ/IWFBvylhN5B4oNeceJ7ECxITtO5BEUG/LIidyDYkPuSWT1Ss2gpEQndqzKbaiXeaClSKBl2ynfTbKONuxNjzXdr8C6V/Uu/LVjdz10GlVg9zzm3UkF1j3z9sFG2rFuW3SbdhMb9rYTewAzwI49cGK/FC8rsF96rLRXFVj3WmtBPzvWbX3vwpMde9eJvQc1O9a9R92HFjv2vseOManAHjqxD8TrCqyP1c8qsG673wa7Yse696kO9LdjfazprALrtqfH4MHYse7d6hG02rGPnNjH4qwC+9iJ/Qqsux37lccO+64Cq/bYS7SDDMkfiWDF1lHrFasSaxOg1nPwT4q9JSHfOIR2F2ZYYIaEGTkR+wVi3xPRKhAtb7nywo7m5O+6ubQLRNsTERZ7E9amzv6Doj/WEg/EboHYXULUeaT4rtVYTsm7UC0u5LTYubDmM6a0sN9Yi+R8qLe8CnG/hOC5/YJm/jpFSxhBoabqqL0o9nhGBvRch3hD0ZsapeLhxk0Lq2Cizpyo0IIKnai3FtRbJ2pmQc2cqFML6tSJ0ivfxHU9ZoDWP76LOT3xDGAfuboE4BVsw65zG9ZoAPPnELzAh9RyH/62KfZ2lTrJMJrHfRKzHE9LljiD2lysQbuOCncpvk5ohUUgGfe8L2N8fMLcxlyuObbCi2InD4qMiT+dmOQZFnTQWwxoPTWjc4daFuTdca0Z/nax7lWtGX6PNL4gL55rzfBTKf30HLJ3JLZzDmwbVtNEal/Xm9Lg/AvTUPVLtOuixcW3OpJzBumdNaR/IN/MwTneyw7VWD+63oxGbowvL42vCQ2t59zQczMq6D2x16tqQeORjGXcq+tNZUhpFx1LOfRT0zeDfQbyzah6MxqH4HHtUMw9N+pNZ++kGI2uN6NxLDjvuSBPXtWb0RjSM+tD15vRwGxLT8b5ut7UsqMGOHbW9aZWfUxZYMwB8ZznFu0VZeQnzSS1mPyD+myN6fOv7mOYs3lWxAj1lLRvW00nLPayeomUvxCBVZs2lAP9i5nhg5VpzMWWM75iGaal/X2Vjt7jUfMt0GIAq5/PAFw58wQkVDkJtN4JULzmjLrKI1O4LScOZ8nJEqorW6dOb1Hz5axRue05tbriMj1arccu2euc5t6EfMIWadalh1blG66i6NJQq6QhN70munsn12tZ+5tO3GQJMSlmWp9OhPgkrT5OtWm9bej4ijzlmULhMx89fzHbfCKtDcY8KdkilKWOp9lP5ZHMNtxX14XOcfNnAb1RtFenZDViOpHKnVGoyhazNz6nZ037iM7kkAfT6MN7DCSVieBTM8yiYz49IItq2lsXb9SXytBxPSerq+xxPXpooIcWdPMYZwd2jHtQ60DMcARPHY8o51Khq5Q0nolPi9PRlN5gfUSflCykosH2JipZyLoo+0WJyhtA42zgKN2fxjIdhe+uUHJH/TZ5dOxatvxX6ORWnW/3aI5Xz+bqTMyAuG4R14BWDZ/q8tMyB5Zgbv1ki/zX+lEivyYc0Ya6uD4zOLNexnTiH1EEOyHPOKHV5lod5d5mfmr5E8XpUKizczzNTslCBmT/AtifUpqTAf2YdwfUCTpbhIRspI/diQvvxubrxM45pv24WPCtBj3fIrJlM+Kv6JqrK6e5yBED7wOLpbmtdNIiXzAirpm07npt1+8+iNT3JMxZwhT1XLlK/D+h3+pHzZO1lRmBGsY3kEtbZ3sfKcUsqKMe7fL1Nkj1NaX8uJDhmZRa739apo9Lku1SxIXy4G49AM59emZeOEsykjtf6cP7aF02FylPlvSIoz2hKJ7t/lDuwCj3Ou2Sa7TmujRLhjALpkUUofq6ssjLfOt5lan70c7/L9S1rstaQ4qB0Blc1pArvx9RtGZKmcCs5vn7ilaTXevZUq96PmOaiyNjLX8DrT+H30pu9exHJyxZhZs0B5iCftIa4ZZgpYcfr5slXmpmKlr6WfPTc1L1MlvOE1+zddMx9mljKoc0a85k1kLVz0PjpUHjpacOO3TWqLWo2pUleu6MLTrytNKXXxNunQaUZ07Kbo9MoWIPKc1Yyo/qwEnVHeMr1DsnrU0nrR6sVvM0wFzzPkj7Wl9e3d8Uu3sgbpFv0ycPjOOXAa3SmHwu1VofqTEF5Hxd2ldz9XepBbmHZEGRMt/jxBXDp059KotC0l/KnS0lO68tgrq39Eb2UTa2S/XPVpAjWhM5rUuFuE49Iim/KUewZJE2DJ8joMx/j3wq9jvqY2azt34nQcmf0PEmryrNiyOFMenflXk7WIleD4z4NaCYcCa96xBoNX/DSIExKpNg9yxzekO4y/FJAnu0IdnPVTvFp3hjQ6INknoufu9hYzjq1XPdnFtqxGpsv4KeqHX91m093PwSb44ufuc50evRrjaSPup86fl8tHpylys/1+lhtsRX62NGfczIQkd5ZUxXfO7NhSVqxoUxPlyajaKJ/M0kbyIzn075Ula9FeVypoFtzAuKl1z3QBFh8+6uWr25TxzjCFfohYQ1qXGLixJm41KZHzAtLWalLq7sQ9x6sXY3SoydqGqnUNTN3ULbb7aQEVm/RLhyNtzblL1bilLcWRim0Bd8o7cqPjRpfg4FfwfCFh0qjj65wzb4t9tiR+y9h9sQr2WdM5oBtaAtGCzF3j05znKPeh29Nqib9H04+POIQdcu6WPaSZvKzpTdkpvU/em/ISuQicgpve7ZfAwmF/dIVjk1GU9Mls09mlio7+I0HYvi4DOSMhd/Pnyu4RrFiVDfaWo2BkXdPYIyhyY81D0Gv3euezfnZXKq19cqF18evAuoExeFw5O/6lhF9/OxUJnxRt4/B7QOJzXU1W7xv45D8dGcmvPy5ZbTd81eerx17hfJjCz6w83XjObmM5urOfrzTIvRaW/Jzo/9vqDRm0qN0bx/+uiP6jmgeM0F50Hd0jHenEVaXl8qeC5gkyEV/xF/veD+NsLrgkaVHE0oqXOKamqqh5ua+salbXTqMx+ZNJ0qmcrUdBzRphuxO+JA3IKfncIDbHo7lL9LyX8Ra//+7ABaT8h6qCw6Zw661BZR9kOfog3oWd+frZIY7/Ly3d4OtOBZeIta8Z7vPeqPd307pbFVf4OE1/pdkYpBKSJZPt3T6yqEEZRP3jgHpL7nG9Bdes5i8c2zkcfZoro/tSzRnD5x3ywIK/GhIWWf5upEntXjyQHesO8V+aFA/JraetLO457r4nxYyflwiXNO2ilzODM+q7+bVcVlx+AyKHJnp7JfSnG2Ps+rz43uVnLhO+j1+GENfmhI2Sbtv6JIOBP12bxZDc2ZlMk8YR0LlYlkPWCc2Sved31ke1rD69Rj/Hcq0XcMSfdBlpDy3wGdsGVEL5G62SPp+aZjfSb1do208nuUzy+vXVv+vwxWK8dbG9d+s3H9wdbaFzfl/3PwofiZ+IW4Cmv8t+ILoHYojoDDH8TfxN/FP7bfbv9x+0/bf+auH1yQmJ+K0r/tv/wX8Vu1MQ==</latexit> 3. Single cell genomics
  15. Entropic Regularization Schr¨ odinger’s problem: [1931] Erwin Schrödinger min P1=a,P>1=b

    P i,j d(xi, yj)pPi,j + "Pi,j log(Pi,j) <latexit 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<latexit 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  16. Entropic Regularization Schr¨ odinger’s problem: [1931] Erwin Schrödinger min P1=a,P>1=b

    P i,j d(xi, yj)pPi,j + "Pi,j log(Pi,j) <latexit 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<latexit 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yj <latexit 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Pi,j > 10 3 " <latexit 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" = 0
  17. Sinkhorn’s Algorithm Proposition: <latexit sha1_base64="CAr6Lw+hs0edXn6cKgSuWJP1qY0=">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</latexit> <latexit sha1_base64="CAr6Lw+hs0edXn6cKgSuWJP1qY0=">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</latexit> <latexit 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<latexit

    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<latexit sha1_base64="CAr6Lw+hs0edXn6cKgSuWJP1qY0=">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</latexit> Ki,j def. = e d(xi,yj )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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<latexit sha1_base64="TzmMHppjQPGpkFJfRm72fbNVqls=">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</latexit> min P nP i,j d(xi, yj)pPi,j + "Pi,j log(Pi,j) ; P1 = a, P>1 = b o <latexit 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<latexit 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<latexit sha1_base64="tQGZ+FtykZ5fhP2XyYtnLKz3TZM=">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</latexit> Pi,j = ui Ki,j vj <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="tM9ZoNF+/Iw0I2pZoWiOJ0AgbhI=">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</latexit>
  18. Sinkhorn’s Algorithm Proposition: <latexit sha1_base64="CAr6Lw+hs0edXn6cKgSuWJP1qY0=">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</latexit> <latexit sha1_base64="CAr6Lw+hs0edXn6cKgSuWJP1qY0=">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</latexit> <latexit 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<latexit

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<latexit 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u (Kv) = a <latexit 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sha1_base64="L0a9yaq7SoDrCaDqUKFsvOMilSM=">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</latexit> v (K>u) = b <latexit 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<latexit 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<latexit sha1_base64="UEfo0q7/awH1ZlqoxebmYfYkUMI=">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</latexit> Ki,j def. = e d(xi,yj )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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<latexit sha1_base64="TzmMHppjQPGpkFJfRm72fbNVqls=">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</latexit> min P nP i,j d(xi, yj)pPi,j + "Pi,j log(Pi,j) ; P1 = a, P>1 = b o <latexit 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<latexit 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<latexit sha1_base64="tQGZ+FtykZ5fhP2XyYtnLKz3TZM=">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</latexit> Pi,j = ui Ki,j vj <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="tM9ZoNF+/Iw0I2pZoWiOJ0AgbhI=">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</latexit> P = diag(u)K diag(v) <latexit 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<latexit 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=) <latexit 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<latexit sha1_base64="0h78JjXFym7avQJT/Y7NxpEtnC0=">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</latexit> a = P1 = diag(u)(Kv) = u (Kv)
  19. Sinkhorn’s Algorithm Proposition: <latexit sha1_base64="CAr6Lw+hs0edXn6cKgSuWJP1qY0=">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</latexit> <latexit sha1_base64="CAr6Lw+hs0edXn6cKgSuWJP1qY0=">AABB1nictVzbchu5EYU3l107N29SecrLJFqnvFuOV1a2KpetVK0sybLWtE2blC+7tF28jGjaQw7NIWXZXFWeUnnNL+Q1+Yh8R/4gecovpC/AAENipjGKY5QkDIjT3egBGt0N0L1pMsrmm5v/PPfet779ne++/8H5C9/7/g9++KOLH/74QZYuZv34sJ8m6exRr5vFyWgSH85H8yR+NJ3F3XEviR/2Xu7g5w+P41k2Sift+Ztp/GTcHU5GR6N+dw5Nzy7+tDOPTwC3bM7SaZqNsPX3p88ubmxe3aR/0Xrlmq5sKP2vmX4YHaqOGqhU9dVCjVWsJmoO9UR1VQbla3VNbaoptD1RS2ibQW1En8fqVF0A7AJ6xdCjC60v4fcQnr7WrRN4RpoZofvAJYGfGSAjdQkwKfSbQR25RfT5gihjaxntJdFE2d7A356mNYbWuXoOrRLO9AzF4Vjm6kj9lsYwgjFNqQVH19dUFqQVlDxyRjUHClNow/oAPp9BvU9Io+eIMBmNHXXbpc//RT2xFZ/7uu9C/ZukvAQlUi09+jSn0FXHRD+it7mAz1ieBDgPgUKsx4i116TrMY1+Av2X0H4HyinVjE56UJbUelqJ3IHiQ+6IyH0oPuS+iGxA8SEbIrIJxYdsaiRiZ6RzP74FxYdviZzvQfEh74nI+1B8yPsi8gEUH/KBiPwKig/5lYi8AcWHvCEib0HxIW+JyDYUH7ItIg+h+JCHInIPig+5p5HlK3UGJSU6I2FVbkO9yAMtRQIt26J818k6+rDXA9Z0vwQrr+pd+OvH7gboNC7B7gXMu6MSrDzz9sFG+rGyLbpJu4kPe1PEHsAM8GMPROyX6kUJ9suAlfayBCuvtQb082Nl63sbnvzY2yL2DtT8WHmPugstfuzdgB1jWoJtith76lUJNsTqz0qwst1vgV3xY+V9qg39/dgQa7oowcr29AF4MH6svFs9hFY/9qGIfaROSrCPROxjsO5+7OOAHfZtCdbssRdoBxmSPxLDiq2i1s1XJdamQK0r8E/yvSUh37gH7RJmmGOGhBmLiP0csR+IaOSIRrBcWW5HM/J3ZS6tHNEKRPTyvQlrc7H/IO+PtSQAsZsjdlcQVR4pvmszlmPyLkyLhJznOxfWQsaU5vYba7GeD9WW1yDuFhA8t5/TzL9C0RJGUKipKmrP8z2ekRE9VyFeU/RmRml4yLh5bhVc1ImI6nlQPRH1xoN6I6IWHtRCRB17UMciyq58F9cJmAFW//gulvTEM4B95PISgVewDbvOTVijEcyfJniB96nlLvxtUewtlSrJMJrHfRKzHE8KlngGtaXagHYbFe5SfJ3QCotBMu55V8f4+IS5jaVec2yFT/OdPMozJuF0RiTPMKeD3mJE66kenVvUckreHdfq4W/m697U6uH3SOOn5MVzrR5+rqWfn0H2tsa2z4BtwWqaau3bel0anH9hGqZ+gXZdtLj4Vsd6ziC9k5r0D/SbOTjDe9mhGuvH1uvRyJzxZYXx1aFh9Zw5eq5HBb0n9npNLao9komOe229rgwp7aITLYd9qvtmsM9AvxlTr0ejCR7XDsXcS6ded/ZO89HYej0aDxTnPU/Jkzf1ejSG9Mz6sPV6NDDb0tVxvq3XteyoAY6dbb2uVZ9QFhhzQDznucV6RTPykxaa2oj8g+psjevzr+9jmLN5mscI1ZSsb1tOp5fvZdUSGX8hBqs2rykH+hcLxwcr0liqLTG+Yhnmhf19nY7d41HzDdBiBKufzwCknHkCEpqcBFrvBCheE6Ou4sgMbkvE4Sw5WkF1dOtc9BYtX84aFdueUasUl9nRWj12yF5nNPem5BM2SLOSHhqlb7iMoqShRkFDMr06unur12tR+5sibrqCmOYzrU8nQnySVh2n+rTecnR8SZ/yzKHwmY+dv5htPtLWBmOelGwRylLF0+1n8khuG+6rV5TNcfNnEb1RtFfHZDVGdCKViVGoyRazN76kZ0v7kM7kkAfT6MN7jDSVqeJTM8yiYz49Iovq2luJN+rLZOi4npHVNfa4Gj100EMPun6MswM7xh2otSFmOISndkCUcyHXVUoan6lf5aejKb3B6og+KVhIQ4PtTVywkFVR9vMCldeAxtnAUXo4jVU6Bt9ZoyRH/T55bOxatPyX6OTWnG93aY6Xz+byTMyAuG4R14hWDZ/q8tMqB5Zg6f1ki/zX6lEivzoc0YZKXJ86nFkvEzrxjymCnZJnnNBqk1ZHsbebn1r9xHBqKnN2jqfZKVnIiOxfBPtTSnMyoh/37oA5QWeLkJCNDLE7o9y78fk6I3GOWT9upPhWg51vMdmyBfE3dN3VldFc5IiB94HTlbltdNIgXzAmrjNt3e3art59EGnvSbizhCnauXKZ+H9Mv82PmScbazMCNYxvINO2zvc+UopZUEdd2uWrbZDp60r5US7DUy213f+sTB8VJNuliAvlwd16AJz79My8cJbMSO5srQ/vo1XZXKQ8XdEjjvaIoni2+0O9A6PcV2iX3KA116FZMoRZMM+jCNNXyiKv8q3mVaQeRjv7v1C3ui5qDSlGymZwWUNSfj+maM2VMoFZzfP3Ja0mv9ZnK72q+UxoLo6dtfwNtP4cfhu5zXMYnV7BKlynOcAU7JPVCLdEaz3CeF0v8DIz09Cyz5afnZOml9tylviarZuNsY9rU2nSrDnRWQtTPwuNFw6NF4E6bNNZo9WiaTeW6JkYW7T1aWUovzrc2jUoL0TKskdmUKMAKd1YKozqQKQqx/gG9VaktSnS6sJqdU8D3DUfgvSv9dXV/U2+u0fqBvk2ffLAOH4Z0Codkc9lWqsjNaaAnD/T9tVd/R1qQe49sqBIme9x4orhU6c+ldNc0l/qnS0lO28tgrm39Fr3MTa2Q/VfryHHtCYyWpcG8Rn1iLX8rhzRikW66vgcEWX+u+RTsd9RHTO7ve07iQr+hI03eVVZXhwpTEj/UubtYC16PXDi14hiwoX2rntAq/4bRgqMMZkEv2eZ0RvCXY5PEtij7ZH9XLdTfIo3cSS6SlIv1R8CbAxHvXauu3PLjNiM7RPoiVq3b93XQ+aXBHOU+J3lRK9Lu9pY+6jLleez0erqXa74XKWHxQpfq48F9XEjCxvlFTEd9XkwF5aoHhfGhHCpN4o68teTvI7MfDoVStn0NpSLmQa2Mc8pXpLugSLC591d9npzHwvj6K3R6xHWpcYtEiXMxqU6P+BaWsxKnV/bh7j1fOVulDg7UdlOYai7u4W132whY7J+iZJyNtzblb1TiFLkLAxT6Cu+0VsWH7o0P4eCvyPliw4Nx5DcYQv82221o/bewW2IV7rOGc2IWtAWDFZi764eZ7FHtY5eOdRd+iEcwnmMQNeS9CPaSevKzpRlyV3q4fRfkxWYqViU3vasPwaXizySdU51xjMiyyaPZqTMd3HqjsVwCBlJkUs4Hz7XkEZxpMx3muqNwVCXR1DkUIeHuccQ9s5t7/q8XE7V+lrnEsqDdwFz4mJwePJXHqvYfiEWaua8kXfPAa3DUQV1s1v8r+MwfCyn+rxCuWX0XbMXAW+d+8U6I4v+cP01Y7mFzOZyjuE803x01lvy82O/L6r1plJnNO+ePvqjdg4YXkvFeVBZOsa7s8jKG0oFzwV8MqTqP+of5+RvI7zKaZTJUYeSOacop2Z6yNTMNy59ozOfhchk6ZTJVKRm44gW3YjdUQfqBvzs5B5g3duh/F1K/otY//dnB9B6RNbDZNE5c9ChtpiyH/YUbUDP9v5smcR4l5fv9rahBc/CG9SK93zvUH+869sujK38GyS81m+rVA0KEcnq6Z5dVz0YQfHkjXNA5nu+Ed2l5ywW3zwbB5wtmvtTqxIt6RP5ZkGvFN9zpOzTXJ3qs3o8OcAb9t08PxSpT6mtq+087rkS52Yp5+YK54y0U+Rw4nxWfTerjMuOw2WQ586Odb+U4mx7nledG90t5cJ30Kvxwwr80JGyRdp/SZHwTFVn8xYVNBdaJveEdaJMJpL1gHFmN3/f1ZHtcQWv44Dx3ypF33Ik3QdZepT/juiEbUb0Eq2bPZKebzpWZ1JvVkirv0f57OLGtdX/y2C9crh19XdXr93b2vjiuv5vDj5QP1O/UJdhif9GfQHEmuqQDr3/qv6m/r79ePuP23/a/jN3fe+cxvxEFf5t/+W/mrqpxQ==</latexit> <latexit 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<latexit

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<latexit 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u (Kv) = a <latexit 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sha1_base64="L0a9yaq7SoDrCaDqUKFsvOMilSM=">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</latexit> v (K>u) = b <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="c65tFjuRWb0VgfFjoHmUj+uQL6Q=">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</latexit> Ki,j def. = e d(xi,yj )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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<latexit sha1_base64="TzmMHppjQPGpkFJfRm72fbNVqls=">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</latexit> min P nP i,j d(xi, yj)pPi,j + "Pi,j log(Pi,j) ; P1 = a, P>1 = b o <latexit 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<latexit 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<latexit sha1_base64="tQGZ+FtykZ5fhP2XyYtnLKz3TZM=">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</latexit> Pi,j = ui Ki,j vj <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="tM9ZoNF+/Iw0I2pZoWiOJ0AgbhI=">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</latexit> Theorem: [Sinkhorn 1964] <latexit 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<latexit 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<latexit sha1_base64="gcU/kHyZLcweAP0wHsiW13HNtBs=">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</latexit> (u, v) converges. <latexit 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<latexit 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<latexit 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Richard Sinkhorn P = diag(u)K diag(v) <latexit 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<latexit 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=) <latexit 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<latexit sha1_base64="0h78JjXFym7avQJT/Y7NxpEtnC0=">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</latexit> a = P1 = diag(u)(Kv) = u (Kv)
  20. Sinkhorn’s Algorithm Proposition: <latexit sha1_base64="CAr6Lw+hs0edXn6cKgSuWJP1qY0=">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</latexit> <latexit sha1_base64="CAr6Lw+hs0edXn6cKgSuWJP1qY0=">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</latexit> <latexit 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<latexit

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<latexit 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u (Kv) = a <latexit 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sha1_base64="L0a9yaq7SoDrCaDqUKFsvOMilSM=">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</latexit> v (K>u) = b <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="c65tFjuRWb0VgfFjoHmUj+uQL6Q=">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</latexit> Ki,j def. = e d(xi,yj )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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<latexit sha1_base64="TzmMHppjQPGpkFJfRm72fbNVqls=">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</latexit> min P nP i,j d(xi, yj)pPi,j + "Pi,j log(Pi,j) ; P1 = a, P>1 = b o <latexit 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<latexit 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! Convolution on regular grids, separable kernels. <latexit 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<latexit 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<latexit 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! Parallelizable on GPUs. <latexit 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<latexit 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<latexit 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<latexit 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Matrix/vector multiplications: ! O(n2 /"2) complexity. <latexit 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<latexit 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<latexit 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<latexit 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Pi,j = ui Ki,j vj <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="tM9ZoNF+/Iw0I2pZoWiOJ0AgbhI=">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</latexit> Theorem: [Sinkhorn 1964] <latexit 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<latexit 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<latexit sha1_base64="gcU/kHyZLcweAP0wHsiW13HNtBs=">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</latexit> (u, v) converges. <latexit 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<latexit 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<latexit 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Richard Sinkhorn P = diag(u)K diag(v) <latexit 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<latexit 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=) <latexit 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<latexit 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a = P1 = diag(u)(Kv) = u (Kv)
  21. The Curse of Dimensionality <latexit sha1_base64="AAQHEaTZCo4XtKgRATbvN+r5c2g=">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</latexit> Theorem: <latexit sha1_base64="bQXa5RnTf3JiNE3Mcsaob7eZqxY=">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</latexit> requires

    n ⇠ (1/ )dimension <latexit 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[Dudley 1968] <latexit sha1_base64="vTWjvPBuVpUk9Xxz732SDCXW3lw=">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</latexit> ↵ <latexit sha1_base64="vTWjvPBuVpUk9Xxz732SDCXW3lw=">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</latexit> ↵ <latexit sha1_base64="kAppDnYCtZIqp/kHZtYnyPO+LpM=">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</latexit> n = 1 n P i xi <latexit sha1_base64="8rJS+aIgevIFAyo1RoikENYqprs=">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</latexit> 8 <latexit sha1_base64="qIMVGIw1nrs/iQEzu5dZKAhRR4M=">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</latexit> 23 <latexit sha1_base64="PHdHdo8XGeIr6zZ1ehfD3lTUFPQ=">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</latexit> E|Wp(↵, n) Wp(↵, 1)| 6 Richard 
 Dudley
  22. The Curse of Dimensionality <latexit sha1_base64="AAQHEaTZCo4XtKgRATbvN+r5c2g=">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</latexit> Theorem: <latexit sha1_base64="bQXa5RnTf3JiNE3Mcsaob7eZqxY=">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</latexit> requires

    n ⇠ (1/ )dimension <latexit 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[Dudley 1968] <latexit sha1_base64="vTWjvPBuVpUk9Xxz732SDCXW3lw=">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</latexit> ↵ <latexit sha1_base64="vTWjvPBuVpUk9Xxz732SDCXW3lw=">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</latexit> ↵ <latexit sha1_base64="kAppDnYCtZIqp/kHZtYnyPO+LpM=">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</latexit> n = 1 n P i xi <latexit sha1_base64="8rJS+aIgevIFAyo1RoikENYqprs=">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</latexit> 8 <latexit sha1_base64="qIMVGIw1nrs/iQEzu5dZKAhRR4M=">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</latexit> 23 <latexit sha1_base64="PHdHdo8XGeIr6zZ1ehfD3lTUFPQ=">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</latexit> E|Wp(↵, n) Wp(↵, 1)| 6 Aude Genevay <latexit sha1_base64="AAQHEaTZCo4XtKgRATbvN+r5c2g=">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</latexit> Theorem: <latexit sha1_base64="bqML1+xf+kMBSZuJMdXq4/xbgEk=">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</latexit> [Genevay 2019] <latexit 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E|W" p (↵, n) W" p (↵, 1)| 6 <latexit 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requires n ⇠ (1/")dimension ⇥ (1/ )2 Richard 
 Dudley
  23. x <latexit 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<latexit 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<latexit 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<latexit

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d(x,y) <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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2. Entropic <latexit 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<latexit 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Regularization <latexit 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1. Optimal Transport <latexit 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<latexit 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4. Gromov Wasserstein <latexit sha1_base64="9fqK2kknFwBXfI8mtR1BkfiXw2M=">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</latexit> 3. Single cell genomics
  24. Single Cell Multi-omics <latexit 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cells <latexit 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2 Rd

    Understanding cell diversity: many types, many states for each type. Applications: cancer mutations, dynamic of adaptation, development, … Tissue Dissociation isolation RNA Amplification Sequencing … RNA: expression of the DNA. <latexit sha1_base64="v4HVUJlrkr1NIl1MUAlx55L31yI=">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</latexit> d ⇠ 104
  25. Single Cell Multi-omics <latexit 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cells <latexit 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2 Rd

    Understanding cell diversity: many types, many states for each type. Applications: cancer mutations, dynamic of adaptation, development, … Tissue Dissociation isolation RNA Amplification Sequencing … RNA: expression of the DNA. <latexit 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d ⇠ 104 <latexit 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d ⇠ 105 <latexit 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d ⇠ 105 <latexit 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d ⇠ 102 ATAC: chromatine accessibility Methylation: presence of methyl groups Proteome: presence of proteins geometry of DNA cause of differential expression result of expression
  26. Single Cell Multi-omics <latexit 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cells <latexit 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2 Rd

    Understanding cell diversity: many types, many states for each type. Applications: cancer mutations, dynamic of adaptation, development, … Tissue Dissociation isolation RNA Amplification Sequencing … 10X Multiome (RNA + ATAC) CITE-seq (RNA + proteines) Paired multi-omics: Un-paired multi-omics: next frontier … RNA: expression of the DNA. <latexit 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d ⇠ 104 <latexit 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d ⇠ 105 <latexit 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d ⇠ 105 <latexit 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d ⇠ 102 ATAC: chromatine accessibility Methylation: presence of methyl groups Proteome: presence of proteins geometry of DNA cause of differential expression result of expression
  27. Comparing Distributions for Single Cells il recently, samples contained many

    cells (bulk omics) ay, we can measure omics at the single cell level1. 2 2018 2Lähnemann et al. 2020 Single-cell profiling uncovers cellular heterogeneity • Until recently, samples contained many cells (bulk omics) • Today, we can measure omics at the single cell level1. 2 1Mincarelli et al. 2018 2Lähnemann et al. 2020 <latexit sha1_base64="8h9qfn6MXuBvKOcg4p0NkYUZouc=">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</latexit> Bulk <latexit sha1_base64="xfWO8cpwoNz5R1B8gV9utdLBqVI=">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</latexit> Single cell
  28. Comparing Distributions for Single Cells il recently, samples contained many

    cells (bulk omics) ay, we can measure omics at the single cell level1. 2 2018 2Lähnemann et al. 2020 Single-cell profiling uncovers cellular heterogeneity • Until recently, samples contained many cells (bulk omics) • Today, we can measure omics at the single cell level1. 2 1Mincarelli et al. 2018 2Lähnemann et al. 2020 <latexit sha1_base64="8h9qfn6MXuBvKOcg4p0NkYUZouc=">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</latexit> Bulk <latexit sha1_base64="xfWO8cpwoNz5R1B8gV9utdLBqVI=">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</latexit> Single cell <latexit sha1_base64="pydPpuNuJAJzk3J9ohxA5exGGlo=">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</latexit> ? <latexit sha1_base64="QNHLtJL77Xel7kqDwcr8uqkXoFI=">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</latexit> Cluster cells from a single biopsy. <latexit sha1_base64="NAYrO+hblycchNy+rUEIB63nwtY=">AAAC6XicjVHLLgRBFD3a+z1Y2nQMYTXpEcGOYGFJYphkRma6y0Vnqh/prvbIxA/Y2YmtH7DlR8Qf8BdulZ7EI0J1uvvUufecqnuvF0s/VY7z0mV19/T29Q8MDg2PjI6NFyYm99MoSwRVRCSjpOq5KUk/pIrylaRqnJAbeJIOvNamjh+cUZL6UbinLmM6DNyT0D/2hauYahRm64ouWNduNrf4NDcUND9ve6TOiUJbkJTp2lWjUHRKjln2T1DOQRH52okKz6jjCBEEMgQghFCMJVyk/NRQhoOYuUO0mUsY+SZOuMIQazPOIs5wmW3x94R3tZwNea89U6MWfIrkN2GljTnWRJyXMNan2SaeGWfN/ubdNp76bpf893KvgFmFU2b/0nUy/6vTtSgcY9XU4HNNsWF0dSJ3yUxX9M3tT1UpdoiZ0/iI4wljYZSdPttGk5radW9dE381mZrVe5HnZnjTt+QBl7+P8yfYXyyVl0tLu4vF9Y181AOYxgwWeJ4rWMc2dlBh72s84BFPVsu6sW6tu49UqyvXTOHLsu7fAYBOnkY=</latexit> “Distance” between cells? <latexit sha1_base64="yFN6xhMLWSFTo6y4Ic3WSee5g64=">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</latexit> OT on genes’ space. <latexit sha1_base64="pydPpuNuJAJzk3J9ohxA5exGGlo=">AAACyHicjVHLSsNAFD2Nr1pfVZdugkVwVZIi6s6iG3FVwbSFtkgyndaheZFMlFLc+ANu9cvEP9C/8M6YglpEJyQ5c+49Z+be68W+SKVlvRaMufmFxaXicmlldW19o7y51UyjLGHcYZEfJW3PTbkvQu5IIX3ejhPuBp7PW97oTMVbtzxJRRReyXHMe4E7DMVAMFcS5XS9gXlyXa5YVUsvcxbYOaggX42o/IIu+ojAkCEARwhJ2IeLlJ4ObFiIiethQlxCSOg4xz1KpM0oi1OGS+yIvkPadXI2pL3yTLWa0Sk+vQkpTeyRJqK8hLA6zdTxTDsr9jfvifZUdxvT38u9AmIlboj9SzfN/K9O1SIxwLGuQVBNsWZUdSx3yXRX1M3NL1VJcoiJU7hP8YQw08ppn02tSXXtqreujr/pTMWqPctzM7yrW9KA7Z/jnAXNWtU+rB5c1ir103zURexgF/s0zyPUcY4GHPIWeMQTno0LIzbujPFnqlHINdv4toyHD4JFkLc=</latexit> ?
  29. Comparing Distributions for Single Cells il recently, samples contained many

    cells (bulk omics) ay, we can measure omics at the single cell level1. 2 2018 2Lähnemann et al. 2020 Single-cell profiling uncovers cellular heterogeneity • Until recently, samples contained many cells (bulk omics) • Today, we can measure omics at the single cell level1. 2 1Mincarelli et al. 2018 2Lähnemann et al. 2020 <latexit sha1_base64="8h9qfn6MXuBvKOcg4p0NkYUZouc=">AAACx3icjVHLTsJAFD3UF+ILdemmkZi4Ii0x6pLgRneYCJIgMe0wwITSNu2USIgLf8Ct/pnxD/QvvDMOiUqMTtP2zLn3nJl7rx8HIpWO85qzFhaXllfyq4W19Y3NreL2TjONsoTxBouCKGn5XsoDEfKGFDLgrTjh3sgP+LU/PFPx6zFPUhGFV3IS887I64eiJ5gnFVXLguFtseSUHb3seeAaUIJZ9aj4ght0EYEhwwgcISThAB5Setpw4SAmroMpcQkhoeMc9yiQNqMsThkesUP69mnXNmxIe+WZajWjUwJ6E1LaOCBNRHkJYXWareOZdlbsb95T7anuNqG/b7xGxEoMiP1LN8v8r07VItHDqa5BUE2xZlR1zLhkuivq5vaXqiQ5xMQp3KV4Qphp5azPttakunbVW0/H33SmYtWemdwM7+qWNGD35zjnQbNSdo/LR5eVUrVmRp3HHvZxSPM8QRXnqKNB3gM84gnP1oUVWWPr7jPVyhnNLr4t6+EDdTmQuA==</latexit> Bulk <latexit sha1_base64="xfWO8cpwoNz5R1B8gV9utdLBqVI=">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</latexit> Single cell <latexit sha1_base64="pydPpuNuJAJzk3J9ohxA5exGGlo=">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</latexit> ? <latexit sha1_base64="QNHLtJL77Xel7kqDwcr8uqkXoFI=">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</latexit> Cluster cells from a single biopsy. <latexit sha1_base64="NAYrO+hblycchNy+rUEIB63nwtY=">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</latexit> “Distance” between cells? <latexit sha1_base64="yFN6xhMLWSFTo6y4Ic3WSee5g64=">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</latexit> OT on genes’ space. <latexit sha1_base64="c8Nzu7i/2HdZbRFNoq24LWiMXCg=">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</latexit> Match cells between two biopsies. <latexit sha1_base64="smAhPpTgHUrzBKRMXffs73pgv0w=">AAAC2HicjVHLSsQwFD1TX+N7dJZugoPoaugMoi5FN+4cYV44irQxajDTliYVBhHciVt/wK1+kfgH+hfexAo+EE1pe3LuPSe594aJktr4/nPBGxoeGR0rjk9MTk3PzJbm5ts6zlIuWjxWcdoNAy2UjETLSKNEN0lF0A+V6ITn2zbeuRCplnHUNINEHPaD00ieSB4Yoo5K5d0miyPGhVJ6mekk4KJ6VKr4Vd8t9hPUclBBvhpx6QkHOEYMjgx9CEQwhBUCaHp6qMFHQtwhLolLCUkXF7jCBGkzyhKUERB7Tt9T2vVyNqK99dROzekURW9KSoYl0sSUlxK2pzEXz5yzZX/zvnSe9m4D+oe5V59YgzNi/9J9ZP5XZ2sxOMGGq0FSTYljbHU8d8lcV+zN2aeqDDkkxFl8TPGUMHfKjz4zp9GudtvbwMVfXKZl7Z7nuRle7S1pwLXv4/wJ2vVqba26ulevbG7loy5iAYtYoXmuYxM7aKBF3gPc4wGP3r537d14t++pXiHXlPFleXdvzGyWRQ==</latexit> OT on cells’ space. <latexit sha1_base64="pydPpuNuJAJzk3J9ohxA5exGGlo=">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</latexit> ?
  30. Context and aims OT cell-cell similarity Wasserstein Singular Vectors Paired

    multiomics integration Thesis overview Single-cell profiling uncovers cellular heterogeneity • Until recently, samples contained many cells (bulk omics) • Today, we can measure omics at the single cell level1. 2 1Mincarelli et al. 2018 2Lähnemann et al. 2020 Comparing Two Cells with OT 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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cell profiling uncovers cellular heterogeneity Until recently, samples contained many cells (bulk omics) Today, we can measure omics at the single cell level1. 2 et al. 2018 2Lähnemann et al. 2020 a <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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sparse <latexit 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noisy
  31. Context and aims OT cell-cell similarity Wasserstein Singular Vectors Paired

    multiomics integration Thesis overview Single-cell profiling uncovers cellular heterogeneity • Until recently, samples contained many cells (bulk omics) • Today, we can measure omics at the single cell level1. 2 1Mincarelli et al. 2018 2Lähnemann et al. 2020 Comparing Two Cells with OT 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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cell profiling uncovers cellular heterogeneity Until recently, samples contained many cells (bulk omics) Today, we can measure omics at the single cell level1. 2 et al. 2018 2Lähnemann et al. 2020 a <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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<latexit 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<latexit 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<latexit 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<latexit 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min P1=a,P>1=b P i,j d(xi, xj) Pi,j <latexit 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sparse <latexit 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noisy <latexit 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Wd(a, b) , <latexit 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Wd(a, b)
  32. Context and aims OT cell-cell similarity Wasserstein Singular Vectors Paired

    multiomics integration Thesis overview Single-cell profiling uncovers cellular heterogeneity • Until recently, samples contained many cells (bulk omics) • Today, we can measure omics at the single cell level1. 2 1Mincarelli et al. 2018 2Lähnemann et al. 2020 Comparing Two Cells with OT 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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cell profiling uncovers cellular heterogeneity Until recently, samples contained many cells (bulk omics) Today, we can measure omics at the single cell level1. 2 et al. 2018 2Lähnemann et al. 2020 a <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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<latexit 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<latexit 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<latexit 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<latexit 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min P1=a,P>1=b P i,j d(xi, xj) Pi,j <latexit 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Bio-inspired <latexit 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Data-driven <latexit 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(e.g. via regulation networks) <latexit 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Choice of <latexit 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gene’s distance <latexit 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d(xi, xj) <latexit 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d(xi, xj) <latexit 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sparse <latexit 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noisy <latexit 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Wd(a, b) , <latexit sha1_base64="/Wd65ZpzfGzd2XBzBQtKW7TJ4Qg=">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</latexit> Wd(a, b)
  33. Paired Multi-omics Integration > pip install mowgli <latexit sha1_base64="Bjs9jbebFK4Ts0ALJxJMWrUF2Sc=">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</latexit> H

    (ATAC) <latexit 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wk <latexit 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⇡ <latexit 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⇥ <latexit 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a(ATAC) k <latexit 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a(RNA) k <latexit 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⇡ <latexit 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H (RNA) <latexit 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(wk)k > 0 <latexit 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min (H( )) >0 X X k W d (H ( ) wk, a ( ) k )
  34. Paired Multi-omics Integration > pip install mowgli <latexit sha1_base64="Bjs9jbebFK4Ts0ALJxJMWrUF2Sc=">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</latexit> H

    (ATAC) <latexit 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wk <latexit 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⇡ <latexit 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⇥ <latexit 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a(ATAC) k <latexit 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a(RNA) k <latexit 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⇡ <latexit 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H (RNA) <latexit 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clustering <latexit 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(wk)k > 0 <latexit 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min (H( )) >0 X X k W d (H ( ) wk, a ( ) k )
  35. Paired Multi-omics Integration > pip install mowgli <latexit sha1_base64="Bjs9jbebFK4Ts0ALJxJMWrUF2Sc=">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</latexit> H

    (ATAC) <latexit 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wk <latexit 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⇡ <latexit 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⇥ <latexit 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a(ATAC) k <latexit 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a(RNA) k <latexit 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⇡ <latexit 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H (RNA) <latexit 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clustering <latexit 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Gene set <latexit 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enrichment <latexit 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(wk)k > 0 <latexit 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min (H( )) >0 X X k W d (H ( ) wk, a ( ) k )
  36. OT Across Cells <latexit 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day 1 <latexit 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day

    18 <latexit sha1_base64="vh31vAG5AzHYBeJ+kRgiWs/Cvbc=">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</latexit> [Schiebinger et al 2019] <latexit sha1_base64="E7xwgtYw1POYNmjFBGWIgnslFAY=">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</latexit> [Waddington, 1936] Conrad Waddington
  37. x <latexit 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<latexit 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<latexit

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d(x,y) <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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2. Entropic <latexit 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<latexit 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Regularization <latexit 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1. Optimal Transport <latexit 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<latexit 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4. Gromov Wasserstein <latexit sha1_base64="9fqK2kknFwBXfI8mtR1BkfiXw2M=">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</latexit> 3. Single cell genomics
  38. Gromov-Wasserstein ↵ 2 M1 + (X) and dX distance on

    X. <latexit 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<latexit 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<latexit 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<latexit 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Metric measure space X , (X, ↵, dX ): X <latexit 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x <latexit 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x0
  39. Gromov-Wasserstein ↵ 2 M1 + (X) and dX distance on

    X. <latexit 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<latexit 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<latexit 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<latexit 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Metric measure space X , (X, ↵, dX ): X <latexit 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x0 [Memoli 2011]<latexit 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[Sturm 2011] <latexit sha1_base64="oDSbclDecgWv8h9r/GWp6jqC/ec=">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</latexit> GW2 2 (X, Y) def. = <latexit sha1_base64="TsngS446EAlSJmDVyPstZmHXnPI=">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</latexit> min P1=a,P>1=b hQP, Pi <latexit sha1_base64="hPciGpqVMnvJnUj42WG5Sjabfec=">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</latexit> def. = X i,i0,j,j0 |dX (xi, xi0 ) dY (yj, yj0 )|2Pi,jPi0,j0
  40. Gromov-Wasserstein ! non-convex, NP-hard . . . <latexit sha1_base64="ggcMBMVGAVaQVaHnsBSwPgZxe5I=">AABFoHictVzvctu4EUeu/67pn8u1H/uFjZNOruO4tnudduamM5fYju2LL1Ei2fmnJENKtKyEFhVSkp3o/BJ9mn7rtG/RN2g/9RW6uwAIUAK5oJuGYxsE8dtdLIHF7gJMNE6G+WR9/Z9XPvne93/wwx99+uOrP/npz37+2bXPf3GUp9OsFx/20iTNnkZhHifDUXw4GU6S+Ok4i8PTKImfRG+38PmTWZzlw3TUmbwfxy9Pw8FoeDzshROoen1t9UY3SUeDbDg4mYRZlp7dCEbp6HYvHc3i89XgQev2SZj1g27STyf562sr62vr9C9YLmyowopQ/1rp59fXRFf0RSp6YipORSxGYgLlRIQih+uF2BDrYgx1L8Uc6jIoDel5LC7EVcBOoVUMLUKofQu/B3D3QtWO4B5p5oTuAZcEfjJABuImYFJol0EZuQX0fEqUsbaK9pxoomzv4W+kaJ1C7UScQC2H0y19cdiXiTgWf6I+DKFPY6rB3vUUlSlpBSUPrF5NgMIY6rDch+cZlHuE1HoOCJNT31G3IT3/F7XEWrzvqbZT8W+S8iZcgWir3qcFhVDMiH5Ab3MKz6Q8CXAeAIVY9RFLZ6TrU+r9CNrPof4BXBdU0jqJ4JpT7UUtcgsuF3KLRe7C5ULussgDuFzIAxbZgsuFbCkkYjPSuRvfhsuFb7OcH8HlQj5ikY/hciEfs8gjuFzIIxb5HC4X8jmLvAeXC3mPRd6Hy4W8zyI7cLmQHRZ5CJcLecgid+ByIXcUsnqmZnClRGfIzMo7UC7zQEuRQM0dVr67ZB1d2Lsec7pXgeVn9Tb8dWO3PXQaV2B3PMbdcQWWH3m7YCPdWN4W7dFq4sLusdh9GAFu7D6L/Ua8qcB+4zHT3lZg+bl2AO3cWN76fgt3buy3LPYBlNxYfo16CDVu7EOPFWNcgW2x2EfiXQXWx+pnFVje7rfBrrix/DrVgfZurI81nVZgeXt6BB6MG8uvVk+g1o19wmKfivMK7FMW+wysuxv7zGOF/VCB1WvsVVpBBuSPxDBj66iFxazE0hiohQz/pFhbEvKNI6jnMIMCMyDMKYvYLRC7noiDAnHgLVde2NGc/F2eS7tAtD0RUbE2YWnCtu8X7bGUeCC2C8T2AqLOI8V3rfsyI+9C13DISbFyYcmnT2lhv7EUq/FQb3k14mEJIcf2CY38VYqWMIJCTdVROynWeIkM6L4OcUbRm+6l5sHjJoVVsFHnLCpyoCIW9d6Bes+ipg7UlEXNHKgZizIz38Z1PUaA0T++izndyREgfeTqKwCv4A6sOnswRwMYPy3wAh9TzUP426bYm7vqJMNoHtdJzHK8LFniDEpzsQL1Jircpvg6oRkWg2Sy5UMV4+Md5jbmas5JK3xRrORBkTHxpzMkeQYFHfQWA5pPzejcp5oL8u5kqRl+r5j3utQMv0MavyAvXpaa4SdK+sklZO8obOcS2DbMprHSvik3pSHzL5KGLl+lVRctLr7VUzVmkN55Q/r76s3sX+K9bFFJ6seUm9HIrf7lpf41oWH0nFt6bkYFvSfp9epS0LgnIxX3mnJTGVJaRUdKDnPX9M1gm756M7rcjEYLPK4tirnnVrnp6B0XvTHlZjSOhMx7XpAnr8vNaAzoXurDlJvRwGxLqOJ8U25q2VEDMnY25aZWfURZYMwByTEva4xXlJGfNFXUhuQf1GdrbJ9/eR3DnM2rIkaop2R822o6UbGW1Uuk/YUYrNqkoRzoX0wtH6xMYy422fhKyjApre/LdMwaj5o/AC0GMPvlHgCXM09AQp2TQOudAMUNNuoq90zjNlkcjpLjBVRX1U5Yb9HwlVmjct1rquXiMtNbo8cu2eucxt6YfMID0iynh4PKN1xFkdPQQUlDPL0muvug5mtZ++ssbryAGBcjrUc7QnInrT5OdWm9ben4ptrlmcAl93zM+MVs87GyNhjzpGSLUJY6nnY7nUey63BdXRUmxy2fBfRG0V7NyGoMaUcqZ6NQnS2W3vic7g3tQ9qTQx6SRg/eY6CojIXcNcMsOubTA7Kotr3leKO+dIZOlnOyutoe16MHFnrgQDePcbZgxXgApQ7EDIdw1/GIcq4WukpJ45m4XeyOpvQG6yP6pGQhNQ1pb+KShayLsk9KVM4AjaNBRun+NBbpaHx3iRIf9bvkMbFr2fLfpJ1bvb8d0hivHs3VmZg+cd0krgHNGrmrK+8WOUgJ5s4nm+S/1vcS+TXhiDaU4/rK4iz1MqId/5gi2DF5xgnNNm52lFvb+anFJ5pTS+i9c9zNTslCBmT/AlifUhqTAf3YZwf0Drq0CAnZSB+7Myy8G5evM2THmPHjhkKeajDjLSZbNiX+mq49u3IaizJikOvAxcLY1jo5IF8wJq6Zsu5mbtevPog05yTsUSIpmrFyi/h/Qb/1jx4nK0sjAjWMbyBXts71PlKKWVBHIa3y9TZIt7WlvFHI8EpJbdY/I9ONkmTbFHGhPLha94Fzj+4lLxwlGcmdL7WR62hdNhcpjxf0iL09pihe2v2BWoFR7lVaJVdoznVplAxgFEyKKEK35bLIi3zreZWp+9HO/y/Uja7LWkOKgTAZXKkhLr8fU7RmS5nAqJbj9y3NJrfWs4VW9XxGNBZPrbn8HdT+Gn5rufW9H52oZBXu0hiQFMyd0YisCZZa+PG6W+KlR6amZe4NPzMmdSu75jLxtbRuJsaeNabSolFzrrIWunwZGm8sGm88ddihvUajRV2vLdFrNrboqN1KX35NuHUaUJ6ylHmPTKOGHlLasZQf1T5LlY/xNeoDS2udpRXCbLV3A+w574N0z/XF2f1dsboH4h75Nj3ywGT80qdZOiSfS9fWR2qSAnL+UtlXe/Z3qQa5R2RBkbI8x4kzRu469ei6KCT9jVrZUrLzxiLoc0tnqo22sV0q/34JeUpzIqd5qRFfUotYyW/LESxYpDXL5wgo8x+STyX9jvqY2W5t3klQ8idMvClnleElI4UR6Z/LvO0vRa/7VvwaUEw4Vd51BLSav2GkIDE6k+D2LHN6Q7jKyZ0E6dFGZD+X7ZTcxRtZEq2R1HPxZw8bI6NeM9btsaV7rPv2W2iJWjdv3dWC55d4c+T4XWZHL6RV7VT5qPOF+8vRCtUqV76v08N0ga/Rx5Ta2JGFifLKmK74ypuLlKgZF4nx4dKsF03kbyZ5E5nl7pQvZd1aUy5nGqSNOaF4iTsHigiXd3fL6c19wfQjWqIXEdamJms4SpiNS1V+wLa0mJUKFiIku55bkxJrPapaLwwPe9UwdlxaypisYCK43I1sbfehW4pW+GyMpNAT8mRvVZxo0/wKLvwdCFeUqDn65BDb4OfeEVti5yOcininyjKzGVAN2oT+Qgweqn6WW9Tr6J1F3abvw8GfxxB0zUk/pBW1qeySMi+5Td2f/hlZg0zErPSmZfM+2Fz4nixzatKfIVk4vjdDob/JadoXzcGnJ2Uu/nzk/gbXi2Ohv21q1gdNne9BmUMTHvo8g987N62b87I51etrmYsvD7kO6J0XjcMdwOqYxbTzsVCZ9UY+Pge0Dsc11PVq8b/2Q/MxnJrz8uWW0zdnbzzeumwXq8ws+sXN54zh5jOaqzn680yL3hmvyc1P+n9BozeVWr35+PTRLzVjQPOaC5kP5aWTeHsUGXl9qeD+gEuGVPxH/O0K/1XCu4JGlRxNKOn9impqugVPTX956eqdfuYjk6FTJVOZmokn2nQydkvsi3vws1V4gE1PicpvKuVfxLq/o+1D7TFZD51NlxmELtXFlAUxu2l9ujfnaKskxjO98oxvB2pwT/yAavG87wNqj2d+O6W+VX9JIuf6tyIV/VJksrjLZ+ZVBD0o78DJXJD+3jegM/UymyVPoJ167DHKc1QyUtJfP88J0ae4cFHSOSH0aKmjHDkpR3QmKa6gHZX61qMRPlY7/bjvgOfzwyK7FIjfUV2oVgdcqTmpWg6pXlBmICL9r0OE9gexCn9XVdktaWtJ0pzeQVmic+tZ/UmwC+e4MF8z3qQ8mM7UzVS7lKJ6s3tYn4ndruQiT7zX4wc1+IElZZve1luKuzNRnzuc1tCcKpns/dyR0HlPqQeMZsNifNTHz7MaXjOP/t+vRN+3JN0FWSLKtge0n5cRvUTpZoekl+cq6/O2ezXS6q82JU1zstKMA31Gso4DflW2xcx++eVZ/cqAX5i56dhz/ZnHvgv2hJNInszkskexh0TyjCh3fmXopMRbjLHH+YzQo7d8X316ylGZspJMPb6NnnnIMvOgc8xIc8xSGLCSKIv1+trKxuL/PrJcONpc21hf23i0ufL1XfU/k3wqfiWui1uwGv9RfA0zsiUOgdNfxF/F38U/dq7v7O083Hkkm35yRWF+KUr/dp7/F/zmbHM=</latexit> <latexit

    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if dX = || · ||, dY = || · ||: concave! ↵ 2 M1 + (X) and dX distance on X. <latexit 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<latexit 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<latexit 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Metric measure space X , (X, ↵, dX ): X <latexit 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x0 [Memoli 2011]<latexit 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[Sturm 2011] <latexit sha1_base64="oDSbclDecgWv8h9r/GWp6jqC/ec=">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</latexit> GW2 2 (X, Y) def. = <latexit sha1_base64="TsngS446EAlSJmDVyPstZmHXnPI=">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</latexit> min P1=a,P>1=b hQP, Pi <latexit sha1_base64="hPciGpqVMnvJnUj42WG5Sjabfec=">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</latexit> def. = X i,i0,j,j0 |dX (xi, xi0 ) dY (yj, yj0 )|2Pi,jPi0,j0
  41. Gromov-Wasserstein ! non-convex, NP-hard . . . <latexit sha1_base64="ggcMBMVGAVaQVaHnsBSwPgZxe5I=">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</latexit> <latexit

    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if dX = || · ||, dY = || · ||: concave! ↵ 2 M1 + (X) and dX distance on X. <latexit 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<latexit 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<latexit 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Metric measure space X , (X, ↵, dX ): X <latexit 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sha1_base64="6XcTMNLhOkSkELp7a9v5fVQsQH4=">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</latexit> up to isometries. <latexit sha1_base64="fcW1dR7VxF9OmMhK+EQAhlodyGE=">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</latexit> Theorem: GW is a distance X <latexit 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<latexit 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x0 [Memoli 2011]<latexit 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[Sturm 2011] <latexit sha1_base64="oDSbclDecgWv8h9r/GWp6jqC/ec=">AABFu3ictVzbchu5EYU3t41y8yaPeZms1ilvSlFkxblUbW3V2pIsay3bsknJ9pq2ikMOKdojkubNsrn8pHxDPiJPqUrek6f8QvoCDDAkZhqjOJ6ShMHgdDd6gEZ3A+N4mPbGk62tv1/56Dvf/d73f/DxD9d+9OOf/PRnVz/5+cl4MB21kuPWIB2MnsbNcZL2+snxpDdJk6fDUdI8j9PkSfx6B58/mSWjcW/Qr0/eDZMX581uv9fptZoTqDq9ut+YJBeT+f6Txen2y+3r8waRnI+S9qJx3pycxfH86WKxYerjdJpkD54tFp+vNZI37aSzdnp1fWtzi/5Fq4UburCu9L+jwSefbqqGaquBaqmpOleJ6qsJlFPVVGO4nqsbaksNoe6FmkPdCEo9ep6ohVoD7BRaJdCiCbWv4XcX7p7r2j7cI80xoVvAJYWfESAjdQ0wA2g3gjJyi+j5lChjbRHtOdFE2d7B31jTOofaiTqDWglnWobisC8T1VF/pj70oE9DqsHetTSVKWkFJY+cXk2AwhDqsNyG5yMotwhp9BwRZkx9R9026fm/qCXW4n1Lt52qf5OU1+CKVE33fpBRaKoZ0Y/obU7hGcuTAucuUEh0H7H0lnR9Tr3vQ/s51D+Aa0Elo5MYrjnVLkqRO3D5kDsich8uH3JfRB7C5UMeisgjuHzII41E7Ih07sfX4PLhayLnR3D5kI9E5GO4fMjHIvIELh/yRER+A5cP+Y2IvAOXD3lHRN6Dy4e8JyLrcPmQdRF5DJcPeSwi9+DyIfc0snimjuAaEJ2eMCtvQTnPAy1FCjW3RPluk3X0YW8HzOlWAVae1bvw14/dDdBpUoDdCxh3nQKsPPL2wUb6sbItukuriQ97V8QewAjwYw9E7NfqVQH264CZ9roAK8+1Q2jnx8rW9z7c+bH3RewDKPmx8hr1EGr82IcBK8awAHskYh+pNwXYEKs/KsDKdr8GdsWPldepOrT3Y0Os6bQAK9vTE/Bg/Fh5tXoCtX7sExH7VF0UYJ+K2Gdg3f3YZwEr7PsCrFlj12gF6ZI/ksCMLaPWzGYlloZArSnwT7O1JSXfOIZ6CdPNMF3CnIuI/QyxH4g4zBCHwXKNMzs6Jn9X5lLLELVARJytTViaiO3bWXsspQGI3Qyxu4Qo80jxXZu+zMi7MDUScpKtXFgK6dMgs99YSvR4KLe8BvEwh+CxfUYjf4OiJYygUFNl1M6yNZ6REd2XId5S9GZ6aXjIuElmFVzUhYiKPahYRL3zoN6JqKkHNRVRMw9qJqLszHdxjYARYPWP72JOdzwC2EcuviLwCm7BqnMX5mgE4+cIvMDHVPMQ/tYo9pauMskwmsd1ErMcL3KWeASluVqHehsV7lJ8ndIMS0AybvlQx/h4h7mNuZ5zbIUX2UoeZRmTcDo9kqeb0UFvMaL5VI3OPapZkHfHpWr4u9m8N6Vq+D3S+IK8eC5Vw0+09JNLyF7X2PolsDWYTUOtfVuuSoPzL0zDlNdo1UWLi2/1XI8ZpHdRkf6BfjMHl3gvO1Ri/dhyNRpjp3/jXP+q0LB6Hjt6rkYFvSf2ek0pqtyTvo57bbmqDANaRftaDntX9c1gm7Z+M6ZcjcYReFw7FHPPnXLV0TvMemPL1WicKM57LsiTN+VqNLp0z/qw5Wo0MNvS1HG+LVe17KgBjp1tuapV71MWGHNAPOa5xnpFI/KTpppaj/yD8myN6/OvrmOYs3mZxQjllKxvW0wnztaycomMv5CAVZtUlAP9i6njg+VpzNW2GF+xDJPc+r5Kx67xqPlD0GIEs5/3AKSceQoSmpwEWu8UKN4Qo658zwxuW8ThKOksoRq6diJ6i5YvZ43ydadUK8VltrdWjw2y12Mae0PyCQ9Js5IeDgvfcBFFSUOHOQ3J9Kro7r2er3ntb4m44RJimI20Fu0I8U5aeZzq03rN0fE1vcszgYv3fOz4xWxzR1sbjHkGZItQljKebjuTR3LrcF3dUDbHzc8ieqNor2ZkNXq0IzUWo1CTLWZvfE73lvYx7ckhD6bRgvcYaSpDxbtmmEXHfHpEFtW1txJv1JfJ0HF5TFbX2ONydNdBdz3o6jHODqwYD6BUh5jhGO7qAVHOWqarAWl8pH6b7Y4O6A2WR/RpzkIaGmxvkpyFLIuyz3JU3gIaRwNH6eE0lukYfGOFkhz1++SxsWve8l+jnVuzv92kMV48moszMW3iuk1cI5o1vKvLd8scWIK598k2+a/lvUR+VTiiDZW4vnQ4s176tOOfUAQ7JM84pdkmzY58azc/tfzEcDpSZu8cd7MHZCEjsn8RrE8DGpMR/bhnB8wOOluElGxkiN3pZd6Nz9fpiWPM+nE9xaca7HhLyJZNib+h686uMY1Fjhh4HVgsjW2jk0PyBRPiOtLW3c7t8tUHkfachDtKmKIdK9eJ/+f02/yYcbK+MiJQw/gGxtrW+d7HgGIW1FGTVvlyG2TaulJ+lsnwUktt1z8r02c5yXYp4kJ5cLVuA+cW3TMvHCUjknu80obX0bJsLlIeLukRe9uhKJ7tflevwCj3Bq2S6zTnGjRKujAKJlkUYdpKWeRlvuW88tTDaI//L9StrvNaQ4qRshlc1pCU308oWnOlTGFU8/h9TbPJr/XRUqtyPn0ai+fOXP4Wan8Fv43c5j6MTpyzCrdpDDAFe2c1wjXRSoswXrdzvMzINLTsveVnx6Rp5dZcJr5m62Zj7FllKkc0ai501sKUL0PjlUPjVaAO67TXaLVo6o0lOhVji7rerQzlV4VbvQLlqUhZ9sgMqhcgpRtLhVFti1TlGN+g3ou0tkRaTZit7m6AO+dDkP65vjy7v81W90jdId+mRR4Yxy9tmqU98rlMbXmkxhSQ801tX93Z36Aa5B6TBUXKfI4TZwzvOrXoWmSS/lqvbAOy89YimHNLb3UbY2MbVP79CvKc5sSY5qVB3KQWiZbflSNaskibjs8RUea/ST4V+x3lMbPb2r6TKOdP2HiTZ5XlxZFCn/QvZd4OVqLXAyd+jSgmnGrvOgZa1d8wUmCMyST4PcsxvSFc5XgngT3amOznqp3iXby+I9EmST1XXwbYGI567Vh3x5bpsenbb6Alat2+dV8LmV8azFHid5kdvSataufaR50v3V+OVlOvcvn7Mj1Ml/hafUypjRtZ2Cgvj2moL4K5sETVuDAmhEu1XlSRv5rkVWTm3alQyqa1oZzPNLCNOaN4SToHigifd3fd6819LvQjXqEXE9alxjUSJczGDXR+wLW0mJWKliIkt15ak1JnPSpaLywPd9WwdpwtZUJWMFVS7oZbu31o5KIVORvDFFqKT/YWxYkuzS/gwt+R8kWJhmNIDrEGfu4ttaP2PsCpiDe6zJnNiGrQJrSXYvCm7me+RbmO3jjUXfohHMJ59EDXkvQ9WlGrys6UZcld6uH035I1GKlElN62rN4Hl4vck1VOVfrTIwsn96anzDc5VftiOIT0JM8lnA/vb0i96CjzbVO1Phjqcg/yHKrwMOcZwt65bV2dl8upXF+rXEJ58Dpgdl4MDncAi2MW2y7EQo2cN/LhOaB16JRQN6vF/9oPw8dyqs4rlNuYvjl7FfDWuV2iM7PoF1efM5ZbyGgu5hjOc5D1znpNfn7s/0WV3tTA6c2Hp49+qR0DhtdccT5Ulo7x7iiy8oZSwf0BnwwD9R/11yvyVwlvMhpFclShZPYriqmZFjI18+Wlr3fmWYhMlk6RTHlqNp6o0cnYHXWg7sDPTuYBVj0lyt9U8l/E+r+jbUNth6yHyaZzBqFBdQllQexuWpvu7TnaIonxTC+f8a1DDe6JH1Itnvd9QO3xzG8917fiL0l4rt9XA9XORSbLu3x2XsXQg/wOHOeCzPe+EZ2p52wWn0A7D9hj5HNUHCmZr5/nhGhTXLgs6ZwQZrSUUY69lGM6k5QU0I5zfWvRCB/qnX7cd8Dz+c0suxSp31FdU68OuFJLUh15pHpOmYGY9L8FEdof1Ab83dBlv6RHK5KO6R3kJbpwnpWfBFt4x4X9mvEa5cFMpm6m2w0oqre7h+WZ2N1CLnzivRzfLcF3HSlr9LZeU9w9UuW5w2kJzamWyd3P7SuT92Q9YDTbzMZHefw8K+E1C+j/vUL0PUfSfZAlpmx7RPt5I6KXat3skfR8rrI8b3u3RFrz1SbTtCcr7TgwZyTLOOBXZTvC7Ocvz8pXBvzCzE/HnevPAvZdsCeSRHwyU8oeJQES8RlR6fxKz0tJthjDgPMZzYDeyn0N6alEZSpKMg34NnoWIMssgE5HkKYjUuiKkmiLdXp1/cby/z6yWjjZ3rzxx82bj26uf3Vb/88kH6tfqk/VdViN/6S+ghl5pI6B01/U39Q/1D/3vtxr7b3aS7npR1c05hcq929v+l9h6Hkk</latexit> GW2 2 (X, Y) def. = <latexit sha1_base64="TsngS446EAlSJmDVyPstZmHXnPI=">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</latexit> min P1=a,P>1=b hQP, Pi <latexit 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def. = X i,i0,j,j0 |dX (xi, xi0 ) dY (yj, yj0 )|2Pi,jPi0,j0
  42. Examples of Applications <latexit sha1_base64="SrVzka0uHt0puaznp5HP0fXKCZQ=">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</latexit> Shape registration: Source Targets Figure

    1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring of cor- ds that metric ransfer mind, at opti- ective. rtation, able to ix. We rgence tasks. frame- stance on, and Source Targets Figure 1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring <latexit 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Y <latexit 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Y <latexit 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Y <latexit 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?
  43. Examples of Applications <latexit sha1_base64="SrVzka0uHt0puaznp5HP0fXKCZQ=">AABB33ictVzNchu5EYY3f2vnz5scU6maROuUN+U4staVzWYrVStLsqy1bNMmJXt3abuG5IiiPeTQM6Qsm6tTDrmlcs0j5Jo8QJ4jb5Cc8grpH2CAITEDQNkIJQqDwdfd6AEa3Y2hetN0VMzW1/954Z1vfPNb3/7Ouxcvffd73//BDy+/96PDIpvn/eSgn6VZ/qQXF0k6miQHs9EsTZ5M8yQe99Lkce/lFt5/fJLkxSibdGZvpsnTcTycjI5G/XgGTc8v/7Q7S04Bt2gfx9MkypMh8Mzp5u/OoueX19avr9NPtFq5IStrQv60sveiA9EVA5GJvpiLsUjERMygnopYFFC+FDfEuphC21OxgLYcaiO6n4gzcQmwc+iVQI8YWl/C5xCuvpStE7hGmgWh+8Alhd8ckJG4ApgM+uVQR24R3Z8TZWyto70gmijbG/jbk7TG0DoTx9Dqwqmevjgcy0wcid/SGEYwpim14Oj6ksqctIKSR8aoZkBhCm1YH8D9HOp9Qio9R4QpaOyo25ju/4t6Yite92Xfufg3SXkFSiTacvRZSSEWJ0Q/oqc5h3ssTwqch0AhkWPE2mvS9ZhGP4H+C2i/D+WMakonPSgLaj1rRG5BsSG3nMhdKDbkrhO5D8WG3HciW1BsyJZEIjYnndvxbSg2fNvJ+SEUG/KhE/kIig35yIk8hGJDHjqRX0CxIb9wIm9DsSFvO5F3odiQd53IDhQbsuNEHkCxIQ+cyB0oNuSORNav1BxKRnRGjlW5CfUqD7QUKbRsOuW7RdbRhr3lsab7NVj3qt6Gv3bstodOkxrsjse8O6rBumfeLthIO9Zti+7QbmLD3nFi92AG2LF7Tuxn4kUN9jOPlfayButea/vQz451W997cGXH3nNi70PNjnXvUQ+gxY594LFjTGuwLSf2oXhVg/Wx+nkN1m3322BX7Fj3PtWB/nasjzWd12Dd9vQQPBg71r1bPYZWO/axE/tEnNZgnzixn4N1t2M/99hh39Zg1R57iXaQIfkjCazYJmpxuSqxNgVqsYN/Wu4tKfnGPWh3YYYlZkiYsROxWyJ2PRH7JWLfW66itKMF+btuLu0S0fZE9Mq9CWszZ/9B2R9rqQdiu0RsLyGaPFJ81mosJ+RdqBYXclbuXFjzGVNW2m+sJXI+NFtehXhQQfDcPqaZf42iJYygUFNN1I7LPZ6REV03IV5T9KZGqXi4cbPSKpioUyeqZ0H1nKg3FtQbJ2puQc2dqBML6sSJ0ivfxHU9ZoDWPz6LBV3xDGAfub5E4BVswq5zB9ZoBPOnBV7gI2p5AH/bFHu7SpNkGM3jPolZjqcVS5xDbSHWoF1HhdsUX6e0whKQjHs+kDE+XmFuYyHXHFvhs3Inj8qMiT+dEckzLOmgtxjRegqjc5dazsi741oY/k657lUtDL9DGj8jL55rYfiZlH52Dtk7Ets5B7YNq2kqta/roTQ4/8I0VP0S7bpocfGpjuWcQXqngfT35JPZO8dz2aIa60fXw2gUxviKyvhCaGg9F4aew6ig98Rer6pFwSOZyLhX10NlyGgXnUg59FXok8E+A/lkVD2MRgs8ri2KuRdGPXT2TsvR6HoYjUPBec8z8uRVPYzGkK5ZH7oeRgOzLbGM83U91LKjBjh21vVQqz6hLDDmgHjOc4v2inLyk+aS2oj8g+Zsjenzr+5jmLN5VsYIzZS0b1tPp1fuZc0SKX8hAas2C5QD/Yu54YNVaSzEhjO+Yhlmlf19lY7e41Hz+6DFCFY/nwG4cuYpSKhyEmi9U6B4wxl1VUemcBtOHM6SoyVUV7bOnN6i5stZo2rbc2p1xWV6tFqPXbLXBc29KfmE+6RZlx72a59wHUWXhvYrGnLTC9HdW7leq9pfd+KmS4hpOdP6dCLEJ2nNcapN621Dx1fkKc8MCp/56PmL2eYjaW0w5snIFqEsTTzNfiqPZLbhvnpN6Bw334voiaK9OiGrMaITqcIZhapsMXvjC7rWtA/oTA55MI0+PMdIUpkKPjXDLDrm0yOyqKa9dfFGfakMHdcLsrrKHjejhwZ6aEGHxzhbsGPch1oHYoYDuOp4RDmXSl1lpPFc/Ko8Hc3oCTZH9GnFQioabG+SioVsirKPK1ReAxpnA0fp/jSW6Sh8d4WSO+q3yaNj16rlv0Int+p8O6Y5Xj+b6zMxA+K6QVwjWjV8qstXyxxYgoX1zgb5r82jRH4hHNGGurg+MzizXiZ04p9QBDslzzil1eZaHdXeZn5q+Y7i1BLq7BxPszOykBHZvwj2p4zmZES/5rsD6gSdLUJKNtLH7oxK78bm64ycc0z7cSPBbzXo+ZaQLZsTf0XXXF0FzUWOGHgfOFua20on++QLJsQ1l9Zdr+3m3QeR+j0Jc5YwRT1XrhL/D+hT/ap5srYyI1DD+AQKaetszyOjmAV1FNMu32yDVF9TyvdLGZ5JqfX+p2V6vyLZNkVcKA/u1gPg3Kdr5oWzJCe5i5U+vI82ZXOR8nRJjzjaI4ri2e4P5Q6Mcl+jXXKN1lyXZskQZsGsjCJUX1cWeZlvM68qdT/axf+FutZ1VWtIMRI6g8sacuX3E4rWTClTmNU8f1/SarJrPV/q1cxnQnNxbKzlr6D1Z/Cp5FbXfnR6Fatwi+YAU9BXWiPcEq308ON1q8JLzUxFS19rfnpOql5my3nia7ZuOsY+CabSollzKrMWqn4eGi8MGi88ddihs0atRdWuLNFzZ2zRkaeVvvxCuHUCKM+dlN0emUKNPKQ0Yyk/qgMnVXeMr1BvnbTWnbRiWK3maYC55n2Q9rW+vLq/Knf3SNwm36ZPHhjHLwNapSPyuVRrc6TGFJDzTWlfzdXfpRbk3iMLipT5PU5cMXzq1KdyVkr6C7mzZWTntUVQ7y29ln2Uje1S/cMV5JjWREHrUiFuUo9Eym/KES1ZpOuGzxFR5j8mn4r9juaY2eytn0lU8Sd0vMmrSvPiSGFC+ndl3vZWotc9I36NKCacS++6B7TCnzBSYIzKJNg9y4KeEO5yfJLAHm2P7OeqneJTvIkh0XWSeiF+72FjOOrVc92cW2rEamy/hJ6odf3UbT3c/FJvji5+5znRi2lXG0sfdbF0fT5asdzlqtdNepgv8dX6mFMfM7LQUV4V0xWfeHNhicK4MMaHS9goQuQPkzxEZj6d8qWseivK1UwD25hjipdc74EiwubdXbV6cx84xtFbodcjrEmNW1yUMBuXyfyAaWkxK3VxZR/i1ouNu1Fq7ER1O4Wibu4W2n6zhUzI+qXClbPh3qbs3UqU4s7CMIW+4Dd66+JDk+YnUPAzErboUHH0yR22wb/dFFti52t4G+KVrHNGM6IWtAWDpdg7luOs9mjW0SuDuknfh4M/jxHo2iX9iHbSUNmZsltyk7o//ddkBXKROKXXPcPHYHJxj2SVU8h4RmTZ3KMZCfVdnNCxKA4+I6ly8efD5xquURwJ9Z2msDEo6u4RVDmE8FDvMfg9c907nJfJqVlfq1x8efAuoE5cFA5P/upjFd3Px0LlxhP5+jmgdThqoK52i/91HIqP5hTOy5dbQd81e+Hx1LlfIjOy6A+HrxnNzWc213P055mVo9Pekp0f+31R0JPKjNF8/fTRH9VzQPFaCM6DuqVjvDmLtLy+VPBcwCZDJv4j/nHB/W2EVyWNOjlCKKlzinpqqoebmvrGpW106p6PTJpOnUxVajqOaNMbsVtiT9yG363SAwx9O5S/S8l/EWv//uwAWo/IeqgsOmcOutSWUPZDn6IN6Fq/P1snMb7Ly+/2dqAFz8L3qRXf871P/fFd305lbPXfIOG1fk9kYlCJSJZP9/S66sEIqidvnANS3/ON6F16zmLxm2djj7NF9f7UskQLuuN+s6BXi+8ZUvZprk7lWT2eHOAb9nGZH4rEr6ktlnYe91wX51Yt59YS54K0U+VwatxrfjerjsuWwWVQ5s5OZL+M4mx9ntecG92u5cLvoDfjhw34oSFlm7T/kiLhXDRn8+YNNOdSJvOEdSJUJpL1gHFmXD7v5sj2pIHXicf479ai7xqS7oIsPcp/R3TClhO9VOpmh6TnNx2bM6l3GqSV36Ok/27wMf1EXPnopqx8fKP87waHG9dv/Ob6hw831j69Jf/PwbviJ+Ln4iqs8Y/Ep0CtJQ6Awx/EX8XfxN83480/bv5p88/c9Z0LEvNjUfnZ/Mt/ASQLrX8=</latexit> Shape registration: Source Targets Figure

    1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring of cor- ds that metric ransfer mind, at opti- ective. rtation, able to ix. We rgence tasks. frame- stance on, and Source Targets Figure 1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring <latexit 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Y <latexit 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Y <latexit 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Y <latexit 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? <latexit 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[Demetci et al 2020] <latexit 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Single-cell <latexit 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multi-omics: <latexit 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ATAC-seq <latexit 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RNA-seq <latexit 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X <latexit 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Y <latexit sha1_base64="8H4xN4xGPG5ztU4N+maxzHTbjXo=">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</latexit> dim ⇠ 103(genes) <latexit sha1_base64="NRLid9ocOcEHNQq7hjUXkZi7pNg=">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</latexit> dim ⇠ 102(peaks)
  44. Schrodinger GW 566 Extensions of Optimal Transport 566 Extensions of

    Optimal Transport Iterations <latexit 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<latexit 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DC-programming / Konno’s relaxation / Frank-Wolfe / . . . <latexit 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min P1=a,P>1=b hQP, Pi + "H(P) <latexit sha1_base64="AusH0c1u1buhtHsYytSDR72YR88=">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</latexit> C def. = QP <latexit 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min P1=a,P>1=b hC, Pi + "H(P) <latexit 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P <latexit 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(Sinkhorn)
  45. Better modeling the dynamics: use gradient flows Luigi Ambrosio Nicola

    Gigli Giuseppe Savare αt+1 = argmin β W(αt , β) + τf(β) <latexit sha1_base64="LIz5cv8SkqGoJa7sBtLUbjFelcY=">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</latexit> ↵0 <latexit sha1_base64="PDCCocAjh/Bnm69+EKF4dh/DduY=">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</latexit> ↵1 Conclusion: gradient flows for genomics
  46. Better modeling the dynamics: use gradient flows Luigi Ambrosio Nicola

    Gigli Giuseppe Savare αt+1 = argmin β W(αt , β) + τf(β) <latexit 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↵0 <latexit 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↵1 <latexit 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Cost c <latexit 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RNA$RNA <latexit 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Space$ATAC <latexit 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Time t <latexit 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Time t + 1 <latexit 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Potential f Key issues: learning the potential f(β) Integrate several omics Conclusion: gradient flows for genomics