diff --git a/principal.tex b/principal.tex index d9655b5..fd6e34e 100644 --- a/principal.tex +++ b/principal.tex @@ -277,7 +277,7 @@ \end{frame} \begin{frame}{Parameter estimation}{Solution} \emph{Variational EM}~\cite{daudinMixtureModelRandom2008,chabert-liddellLearningCommonStructures2024}. - \begin{block}{Variational approximation of $\mathbf{Z,W|Y},\theta^{(t-1)}$} + \begin{block}{Variational approximation of $\mathbf{Z,W|Y}$} $\mathcal{R}_{Y^m,\tau}(Z^m, W^m) = \mathcal{R}^1_{Y^m,\tau}(Z^m) {\color{red}\times} @@ -286,8 +286,8 @@ \begin{align*} \ell (\mathbf{Y};\theta) \geq \color{red}\sum_{m=1}^{M} \bigg( \color{black} \mathbb{E}_{\mathcal{R}_{Y^m,\tau}(Z^m,W^m)} - \left[ \ell_c(Y^m,Z^m,W^m ; \theta^{(t)}) \right] + \\ - \mathcal{H}(\mathcal{R}_{Y^m,\theta^{(t)}} + \left[ \ell_c(Y^m,Z^m,W^m ; \theta) \right] + \\ + \mathcal{H}(\mathcal{R}_{Y^m,\tau} (Z^m, W^m)) \color{red}\bigg) \color{black} \eqcolon \mathcal{J}(\mathcal{R}_{\mathbf{Y},\tau};\theta)