X-Git-Url: https://www.fleuret.org/cgi-bin/gitweb/gitweb.cgi?p=tex.git;a=blobdiff_plain;f=elbo.tex;fp=elbo.tex;h=175019c5e7d51d55a4a6d01fc4caede268b721aa;hp=239a657f8c438ebf50e970b52d049c2b22a5b498;hb=44313fda41b14cbb410ee9aa1363b0e4ff18f0b7;hpb=43b0cb04eae4537d95775038d9e700e642087d6d

diff --git a/elbo.tex b/elbo.tex
index 239a657..175019c 100644
--- 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 $q$
 %