\end{center}
-Given a training set $x_1, \dots, x_N$ that follows an unknown
+Given i.i.d training 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 $q$
%