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Update.
author
François Fleuret
<francois@fleuret.org>
Sun, 25 Feb 2024 08:58:14 +0000
(09:58 +0100)
committer
François Fleuret
<francois@fleuret.org>
Sun, 25 Feb 2024 08:58:14 +0000
(09:58 +0100)
elbo.tex
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elbo.tex
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Fran\c cois Fleuret
\end{center}
\end{center}
-Given a training
set $x_1, \dots, x_N$ that follows an unknow
n
-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 a
n
+unknown distribution $\mu_X$, we want to fit a model $p_\theta(x,z)$
+
to it,
maximizing
%
\[
\sum_n \log \, p_\theta(x_n).
\]
%
%
\[
\sum_n \log \, p_\theta(x_n).
\]
%
-If we do not have a analytical form of the marginal $p_\theta(x_n)$
+If we do not have a
n
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 $q$
%
but only the expression of $p_\theta(x_n,z)$, we can get an estimate
of the marginal by sampling $z$ with any distribution $q$
%