Confronting_the_partition_function

分配関数との対峙
Chapter 18 in Deep learning Book
深層学習本（Deep learning book by Ian Goodfellow）
URL：http://www.deeplearningbook.org/

Tag: deep learning, machine learning, mathematics, nce, partition function, pcd, sml

Transcript

1. / 1
2. de • x No • k p L i a R I Si • mr • Pc i Lh Tc i • tn Pc i • v • lxN • u M s i gi • ag i gi • 8 9 8 B 8 D • D 6 CD 6 / G E 8 DB CD F8 F8B98 68 • 1C8E 8 • 6 B8 / D6 9 2 D / D6 9 • 8 C 9 6 B8 / D6 9 • C8 DB CD F8 CD D • CD D 9 D 8 1 BD D E 6D • 8 8 - A BD 68 A 9 • B 98 A 9
3. 8 3 6 1 / 8 8 3 1 / 8 6 1 / 8 9 1 / 8
4. 8 / 1 9 46
5. 9 65 1 / 8
7. 7 8 / → / 96 / 1 θ/
8. 9 1 / 6 9 positive phase negative phase → 8
   
   
   
9.  
   
      
   
   
   
10.  
    
     
11. 8 / 16
12. 
    6 8 → 8 3 21 444page 6 / 8 9 6
13. 1 /6 6 ↓ 9 31 /6 6 ↓ 9 8 8 → =0
14. 6 1 6 → 1 9 / 4 4 6 8
15. 5 1 9 8 5 9 / 5 65 9 / 5 5
16. /18 hallucinations fantasy particles 6 9 /
17. 1 9 8 6 7 logZ7 logp~ 1 7 / 7 / 7 1 7 logp~ 1
18. 698 / 2 . 1
19. 9 6 /1 || MCMC1 8 / 6 8 /
20. 9 6C CD 9 6C 1 9D 1 2 8/ 0 9D 0
21. 6 D / 8 CD8 1 9 C D / 2 || 2
22. / 8 9 6 D / C 8 1 9 12 8 9
23. M SML P PCD 9 6 8 C S D 9 312 /L
24. L D2 8 8 6 P 4 M 1 6 9 / C 6 6/ S
25. S C 5 P L M2 SML8 6 CD6 9 D / 15 6
27. 61 2 / 8 7
28. 1 2 1 9 /9 a,b,c 1 68 / • a 1 • b • c 1 8
29. 8 2 / 19 2 1 6
30. 8 
    pseudolikelihood 3 / 6 3 1 p~0 k^n → k*n 9 /
31. 9   
    generalized pseudolikelihood estimator → 8 31 m 6 / m = 1 S(1) = 1,…,n → m = n S(i) = {i} →
32. 1 1 8 26 / 2 6 9 3 / 1 / 1 8 6 9
33. 9 / /1 p~(x)/ 86 31 p~ 3→ / 8 8
34. 4 4 3 / 68 1 8 4 9 3 8 64
35. 5 13/ 13 8 9 6
36. 8 3 3 / SML / 8 3 1 / →SML 8 6 9 16
37. /. 1 /. 1
38. 6 3 98 Z/ 1 1 1
39. 1/ 36 Z → xZ = 0 8 pdata 9
40.   
    
      ||
41. 4 • 
      x4 • logp~(x)1 4 46 • 46 • logp~(x)4 4 / • 8 49 • 4 4 4
42. • 9 4 / • 4 4 2 8 • 21 9 2 9 8 9 /6
43. 31 . /
44. ? pdata ? q(x|y)8 8y6 x 1 4 → 68 pdata48 4 / 4 9
45. 8 • 5/ p model1 6 9 / 4 • / 4 1 6 4 6 • Kingma 1 6 4 8 6
47. a c 7 1 - ,1 4 4 - - 4 / 4 1 8 e c C E e Z c i • 9 –logZ(θ) • ΘE9 c
    c NC6
48. 4 noise distribution p noise(x) 8 E/ 1 p noise(x) 6 96 C
49. 69 4 1 8 1 /
50. 59 p joint 0 p train 8 / 6 1 /
51. p joint E 8 9 C / 615 8 9
52. 98 • logp~ model Back prop • p noise 25 51 6 →NCE /
53. e sl v 1 / 1 3 1 - / 5 • • r a →o c v • ta • ta 6 • 8m f e n i 9 • c sl v • f v c 5 • 6
54. 6 4 • • 5 G 6 8 / • GAN • 5 G A / 1 9 8 G/
56. • 9 • Z 8 6 / • • / ) 6 5( 1
57. • • 5 8 • /1 657 9 657
58. A • 9 2 • 9 • 9 • • 6 8 5 • 6 8 5/ 1 2 B
59. 6 || 6 89 / 1 5
60. 9 6 8 9 9 Z(θ A ) / 01
61. / → 9 691 9 8 / /
62.    
    
     
63. 6 6 6 p0 p1 8 9 3 • p1 / 1 • p1 / 1 p0 / 6 • p0 p1 p0 6 p1 1 Z16 1
64. 1 1 141 / / 8 9 / → /6 1 /
65. p0 p1 6 9 8 p0 p1 / 58 bridge the gap intermediate distributions 8 1. 1 annealed importance sampling, AIS 2. bridge sampling
66. DKL(p0||p1) I p0 p1 9 A6 8 S 1 / 1
67. 69 7 1. Z0 Z1/ 2. Z0 I 1 8 3. A 2 8
68. 8 A 6 8 0 <= j <= n-1 / pnj pnj+1 S → 6 1 8 Znj+1 / Znj →1 8 Z1 / Z0 8 9 → 9 p1 8 p0 8I
69. 8 6 I / 8 9 A Tnj(x’|x) 1 Pnj(x) 1
70. 0 / 7 98 6 01
71. 6 A9 9 8 I / I / 1 7 1 log w(k) 1
72. 6 7 91 A A S 9 7 A 8 / 1 I 9 A 2
73. 3 1 / AIS motivation 8 9 7 61 p* p0 p1 9
74. 4 1 / d
    7 6 7 8 a d be g → be 9 be 6
75. / 1 5 9 7 AIS / 1 6 8 6
76. 89 AIS 1 / / 796 89 /
77. 1 / 1 Desjardins/ 987 6 AIS 6 RBM