% 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}

%%% Local Variables:
%%% mode: tex-pdf
%%% TeX-master: t
%%% End: