From: Francois Fleuret <francois@fleuret.org>
Date: Fri, 10 Dec 2021 21:53:37 +0000 (+0100)
Subject: Update.
X-Git-Url: https://www.fleuret.org/cgi-bin/gitweb/gitweb.cgi?p=pytorch.git;a=commitdiff_plain;h=c16fa89db08b59e454c6ca4b5c68bf7396e876dc

Update.
---

diff --git a/elbo.py b/elbo.py
new file mode 100755
index 0000000..24155fe
--- /dev/null
+++ b/elbo.py
@@ -0,0 +1,29 @@
+#!/usr/bin/env python
+
+# Any copyright is dedicated to the Public Domain.
+# https://creativecommons.org/publicdomain/zero/1.0/
+
+# Written by Francois Fleuret <francois@fleuret.org>
+
+import torch
+
+def D_KL(p, q):
+    return - p @ (q / p).log()
+
+# p(X = x, Z = z) = p[x, z]
+p = torch.rand(5, 4)
+p /= p.sum()
+
+q = torch.rand(p.size())
+q /= q.sum()
+
+p_X = p.sum(1)
+p_Z = p.sum(0)
+p_X_given_Z = p / p.sum(0, keepdim = True)
+p_Z_given_X = p / p.sum(1, keepdim = True)
+q_X_given_Z = q / q.sum(0, keepdim = True)
+q_Z_given_X = q / q.sum(1, keepdim = True)
+
+for x in range(p.size(0)):
+    elbo = q_Z_given_X[x, :] @ ( p_X_given_Z[x, :] / q_Z_given_X[x, :] * p_Z).log()
+    print(p_X[x].log(), elbo + D_KL(q_Z_given_X[x, :], p_Z_given_X[x, :]))