Update.

diff --git a/elbo.tex b/elbo.tex
index 239a657..175019c 100644 (file)
--- a/elbo.tex
+++ b/elbo.tex
@@ -91,15 +91,15 @@ Fran\c cois Fleuret
 
 \end{center}
 
-Given a training set $x_1, \dots, x_N$ that follows an unknown
-distribution $\mu_X$, we want to fit a model $p_\theta(x,z)$ to it,
-maximizing
+Given a training i.i.d train samples $x_1, \dots, x_N$ that follows an
+unknown distribution $\mu_X$, we want to fit a model $p_\theta(x,z)$
+to it, maximizing
 %
 \[
 \sum_n \log \, p_\theta(x_n).
 \]
 %
-If we do not have a analytical form of the marginal $p_\theta(x_n)$
+If we do not have an analytical form of the marginal $p_\theta(x_n)$
 but only the expression of $p_\theta(x_n,z)$, we can get an estimate
 of the marginal by sampling $z$ with any distribution $q$
 %