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% example.tex
%
% Copyright (C) 2010,2011 Laura Dietz
% Copyright (C) 2012 Jaakko Luttinen
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU General Public License.
%
% See the files LICENSE_LPPL and LICENSE_GPL for more details.
\documentclass[a4paper]{article}
\usepackage{tikz}
\usetikzlibrary{bayesnet}
%\pgfrealjobname{example} % name of this file
\title{Graphical Models in Tikz}
\author{Laura Dietz, Jaakko Luttinen}
\begin{document}
\maketitle
TikZ examples for graphical models (Bayesian networks) and directed
factor graphs \cite{Dietz:2010}.
% A table of node types
\begin{table}[ht]
\caption{Node types}
\begin{center}
\begin{tabular}{llc}
Type & Syntax & Output
\\
\hline
Latent variable &
\texttt{\textbackslash node[latent]} &
\tikz{ %
\node[latent] {$x$}; %
}
\\
Observed variable &
\texttt{\textbackslash node[obs]} &
\tikz{ %
\node[obs] {$y$}; %
}
\\
Deterministic &
\texttt{\textbackslash node[det]} &
\tikz{ %
\node[det] {dot} ; %
}
\\
Constant &
\texttt{\textbackslash node[const]} &
\tikz{ %
\node[const] {$a$}; %
}
\\
Factor &
\texttt{\textbackslash node[factor]} &
\tikz{ %
\node[factor] [label=$\mathcal{N}$] {}; %
}
\\
Factor with nodes &
&
\tikz{ %
\node[obs] (y) {$y$} ; %
\node[latent, left=of y, yshift=0.5cm] (mu) {$\mu$} ; %
\node[latent, left=of y, yshift=-0.5cm] (tau) {$\tau$} ; %
\factor[left=of y] {y-factor} {$\mathcal{N}$} {} {};
\factoredge {mu,tau} {y-factor} {y} ; %
}
\\
Plate &
\texttt{\textbackslash plate} &
\tikz{ %
\node[latent] (x) {$x_m$}; %
\plate {} {(x)} {$m \in \mathcal{M}$}; %
}
\\
Gate &
&
\tikz{
% Nodes
\node[obs] (k) {$k$}; %
\node[latent, above=2 of k] (l) {$\lambda$}; %
\factor[above=0.8 of k] {k-f} {Multi} {} {}; %
\node[latent, right=of k-f] (paa) {$\phi$}; %
%\node[latent, right=of k-f] (p) {$\phi$}; %
% Connections
\factoredge {paa} {k-f} {k} ; %
% Gate
\gate {} {(k-f)(k-f-caption)} {l} ; %
}
\end{tabular}
\end{center}
\end{table}
% Simple Bayesian network
\begin{figure}[ht]
\begin{center}
\begin{tabular}{cc}
\input{model_pca} &
\input{model_pca2}
\end{tabular}
\end{center}
\caption{PCA model as a Bayesian network and a directed factor
graph.}
\end{figure}
% Latent Dirichlet allocation
\begin{figure}[ht]
\begin{center}
\input{model_lda}
\end{center}
\caption{Latent Dirichlet allocation as directed factor graph.}
\end{figure}
% Citation influence model
\begin{figure}[ht]
\begin{center}
\input{model_citation_influence}
\end{center}
\caption{Citation influence model with own topics \cite{Dietz:2007}
as directed factor graph.}
\end{figure}
\clearpage
\begin{thebibliography}{9}
\bibitem{Dietz:2010}
Laura Dietz,
\emph{Directed Factor Graph Notation for Generative Models}.
Technical Report. 2010
% Laura Dietz, Steffen Bickel, Tobias Scheffer.
% Unsupervised Prediction of Citation Influences.
% In: Proceedings of International Conference on Machine Learning. 2007
\bibitem{Dietz:2007}
Laura Dietz, Steffen Bickel, Tobias Scheffer,
\emph{Unsupervised Prediction of Citation Influences}.
In: Proceedings of International Conference on Machine
Learning. 2007
\end{thebibliography}
\end{document}
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