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Variational AutoEncoder

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Variational AutoEncoderの概要と設計

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Variational AutoEncoder

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  5. 5. 5 p(x|y) = p(y|x)p(x) p(y) p(x, y) = p(y|x)p(x) p(x) = Z p(x, y)dy
  6. 6. 6 p(✓|D) = p(D|✓)p(✓) p(D) p(x|D) = X ✓ p(x|✓, D)p(✓|D)
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  9. 9. 9 log p(x) = + L = KL(q(z|x)||p(z))L + Eq(z|x)[log p(x|z)] KL(q(z|x)||p(z|x)) log p(x) = log p(x) Z q(z|x)dz = log p(x, z) p(z|x) Z q(z|x)dz = Z q(z|x) log q(z|x) p(z|x) p(x, z) q(z|x) dz = Z q(z|x) log p(z|x) q(z|x) dz + Z q(z|x)log p(x, z) q(z|x) dz = KL(q(z|x)||p(z|x)) + L
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  12. 12. 12 p✓(x|z) p✓(x|z) q (z|x) q (z|x)
  13. 13. 13 q (z|x) p✓(x|z) L(x; ✓, ) = KL(q (z|x)||p(z)) + Eq (z|x)[log p✓(x|z)]
  14. 14. 14 L(x; ✓, ) = KL(q (z|x)||p(z)) + Eq (z|x)[log p✓(x|z)] L(x; ✓, ) = 1 2 dX (1 + log ( 2 d) µ2 d d) + 1 L lX log p✓(x|zl)
  15. 15. 15 z ⇠ N(µ, ) z ⇠ N(µ, )
  16. 16. 16 ✏ ⇠ N(0, I) z = µ + ✏
  17. 17. 17 q (z|x) p✓(x|z)
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