From: François Fleuret Date: Sun, 25 Feb 2024 08:58:14 +0000 (+0100) Subject: Update. X-Git-Url: https://fleuret.org/cgi-bin/gitweb/gitweb.cgi?a=commitdiff_plain;h=44313fda41b14cbb410ee9aa1363b0e4ff18f0b7;p=tex.git Update. --- 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 $q$ %