3 # Any copyright is dedicated to the Public Domain.
4 # https://creativecommons.org/publicdomain/zero/1.0/
6 # Written by Francois Fleuret <francois@fleuret.org>
12 return -a @ (b / a).log()
15 # p(X = x, Z = z) = p[x, z]
17 p_XZ = torch.rand(5, 4)
19 q_XZ = torch.rand(p_XZ.size())
24 p_X_given_Z = p_XZ / p_XZ.sum(0, keepdim=True)
25 p_Z_given_X = p_XZ / p_XZ.sum(1, keepdim=True)
27 # q_X_given_Z = q_XZ / q_XZ.sum(0, keepdim = True)
28 q_Z_given_X = q_XZ / q_XZ.sum(1, keepdim=True)
30 for x in range(p_XZ.size(0)):
31 elbo = q_Z_given_X[x, :] @ (p_X_given_Z[x, :] / q_Z_given_X[x, :] * p_Z).log()
32 print(p_X[x].log(), elbo + D_KL(q_Z_given_X[x, :], p_Z_given_X[x, :]))