From b0aa3b2b98c89b71d86a03d559c640c4b599da85 Mon Sep 17 00:00:00 2001
From: ludwigbothmann <46222472+ludwigbothmann@users.noreply.github.com>
Date: Wed, 22 Nov 2023 13:47:02 +0100
Subject: [PATCH] Updates from Overleaf

---
 slides/information-theory/slides-info-kl.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/slides/information-theory/slides-info-kl.tex b/slides/information-theory/slides-info-kl.tex
index ad41256f..cb71203c 100644
--- a/slides/information-theory/slides-info-kl.tex
+++ b/slides/information-theory/slides-info-kl.tex
@@ -85,7 +85,7 @@
 
 First, we could simply see KL as the expected log-difference between $p(x)$ and $q(x)$:
 
-  $$ D_{KL}(p \| q) = \E_{X \sim p}[\log(p(x)) - \log(q(x))].$$
+  $$ D_{KL}(p \| q) = \E_{X \sim p}[\log(p(X)) - \log(q(X))].$$
 
 This is why we integrate out with respect to the data distribution $p$.
 A \enquote{good} approximation $q(x)$ should minimize the difference to $p(x)$.
@@ -168,7 +168,7 @@
 
 But maybe we want to pose the question "How different is $q$ from $p$?" by formulating it as:
 "If we sample many data from $p$, how easily can we see that $p$ is better than $q$ through LR, on average?"
-$$ \E_p \left[\log \frac{p(x)}{q(x)}\right] $$
+$$ \E_p \left[\log \frac{p(X)}{q(X)}\right] $$
 That expected LR is really KL!
 
 \framebreak