Poster 98% done

1 files changed, 46 insertions, 32 deletions

diff --git a/poster/Finale_poster/poster.tex b/poster/Finale_poster/poster.tex
index 1365801..7865e18 100644
--- a/poster/Finale_poster/poster.tex
+++ b/poster/Finale_poster/poster.tex
@@ -1,6 +1,6 @@
 \documentclass[final]{beamer}
 \usepackage[utf8]{inputenc}
-\usepackage[scale=1.8]{beamerposter} % Use the beamerposter package for laying
+\usepackage[scale=1.7]{beamerposter} % Use the beamerposter package for laying
 \usetheme{confposter} % Use the confposter theme supplied with this template
 \usepackage{framed, amsmath, amsthm, amssymb}
 \usepackage{graphicx}
@@ -16,7 +16,7 @@
 \newlength{\twocolwid}
 \newlength{\threecolwid}
 \setlength{\paperwidth}{48in} % A0 width: 46.8in
-\setlength{\paperheight}{40in} % A0 height: 33.1in
+\setlength{\paperheight}{36in} % A0 height: 33.1in
 \setlength{\sepwid}{0.024\paperwidth} % Separation width (white space) between
 \setlength{\onecolwid}{0.29\paperwidth} % Width of one column
 \setlength{\twocolwid}{0.464\paperwidth} % Width of two columns
@@ -24,7 +24,7 @@
 \setlength{\topmargin}{-1in} % Reduce the top margin size
 
 \title{Bayesian and Active Learning for Graph Inference} % Poster title
-\author{Thibaut Horel\and Jean Pouget-Abadie} % Author(s)
+\author{Thibaut Horel\\[0.5em] Jean Pouget-Abadie} % Author(s)
 
 \begin{document}
 \setlength{\belowcaptionskip}{2ex} % White space under figures
@@ -44,9 +44,9 @@
       \item \textbf{Objective:} learn $\Theta$, matrix of edge weights.
 \end{itemize}
 \end{block}
-\vspace{1cm}
+\vspace{2cm}
 
-\begin{block}{\bf Contagion Model~\cite{}}
+\begin{block}{\bf Contagion Model~\cite{Pouget:2015}}
 \begin{itemize}
     \item $X^t\in\{0,1\}^N$: state of the network at time $t$
     \item At $t=0$, $X^0$ drawn from \emph{source distribution}
@@ -67,6 +67,7 @@
   \end{center}
 \end{figure}
 \end{block}
+\vspace{2cm}
 
 \begin{block}{MLE}
   \begin{itemize}
@@ -81,7 +82,7 @@
     Can be solved efficiently by SGD on $\Theta$.
   \vspace{1cm}
 \item log-likelihood is concave for common contagion models (\emph{e.g} IC
-    model) $\Rightarrow$ provable convergence guarantees (\cite{}).
+    model) $\Rightarrow$ provable convergence guarantees \cite{Netrapalli:2012}.
   \end{itemize}
 \end{block}
 \end{column} % End of the first column
@@ -94,6 +95,7 @@
 \begin{block}{Bayesian Framework}
 \begin{figure}
   \centering
+  \vspace{-1em}
   \includegraphics[scale=3]{graphical.pdf}
 \end{figure}
 {\bf Advantages:}
@@ -113,23 +115,27 @@
   \begin{center}--~OR~--\end{center}
   \emph{Can we cherry-pick the most relevant part of the dataset?}
 
+\vspace{0.5em}
 {\bf Idea:} Focus on parts of the graph which are unexplored (high uncertainty).
-i.e.~maximize information gain per cascade
+i.e.~maximize information gain per observation.
 
-Baseline heuristic:
+\vspace{0.5em}
+\textbf{Baseline heuristic:}
 \begin{itemize}
-  \item Choose source proportional to estimated out-degree $\implies$ wider
+  \item Choose source w.p. proportional to estimated out-degree $\implies$ wider
     cascades $\implies$ more data
 \end{itemize}
 
-Principled heuristic:
+\vspace{0.5em}
+\textbf{Principled heuristic:}
 \begin{itemize}
-  \item Choose source proportional to mutual information
-    \begin{equation*}
-      I((X_t) ,\Theta | x^0 = i) = - H(\Theta | (X_t), X_0 = i) + H(\Theta)
-    \end{equation*}
-  \item Exact strategy requires knowing true distribution of $(X_t)$
-  \item Use estimated $\Theta$ to compute $H(\Theta | (X_t), X_0 = i)$
+  \item Choose source w.p. proportional to mutual information
+      \begin{multline*}
+        p(i) \propto I\big(\{X_t\}_{t\geq 1} ,\Theta | X^0 = \{i\}\big)\\
+        = H(\Theta) - H\big(\Theta | \{X_t\}_{t\geq 1}, X_0 = \{i\}\big)
+    \end{multline*}
+\item Requires knowing true distribution of $\{X_t\}$ $\Rightarrow$ use current
+    estimate of $\Theta$ instead.
 \end{itemize}
 \end{block}
 \end{column}
@@ -142,34 +148,42 @@ Principled heuristic:
   \begin{block}{Implementation}
   {\bf Scalable Bayesian Inference}
   \begin{itemize}
-    \item MCMC (PyMC~\cite{})
-    \item VI (BLOCKS~\cite{})
+    \item MCMC: implements the graphical model directly with PyMC
+        \cite{pymc}; does not scale beyond 10 nodes.
+    \item VI: implements variational inference with  Blocks~\cite{blocks}.
+        (wip: use Bohning bounds to avoid sampling).
   \end{itemize}
 
-  {\bf Scalable Active Learning Criterion}
-Approx.~heuristic:
+  \vspace{1em}
+  {\bf Scalable Active Learning}
+
+  Mutual information is expensive to compute. Instead:
 \begin{itemize}
-  \item Choose source proportional to mutual information of first step of
-    cascade and $\Theta$: Hope for closed-form formula
-  \item Intuition:
-    \begin{itemize}
-      \item Choose lower bound of mutual information $I(X, Y) \geq I(f(X),
-        g(Y))$ where $f$ is the trunctation function
-      \item First step is most informative~\cite{}
-    \end{itemize}
-  \item Sum over outgoing-edges' variance as proxy
+    \item use mutual information between $\Theta$ and $X^1$.
+
+        \textbf{Justification} for any $f$:
+        \begin{displaymath}
+            I(X, Y) \geq I\big(f(X)\big)
+        \end{displaymath}
+        in our case: $f$ truncates the cascade at $t=1$.
+
+        (wip: obtain closed-form formula in this case).
+  \item variance is a lower-bound on mutual information $\implies$ pick
+      node $i$ w.p. proportional to $\sum_j \text{Var}(\Theta_{i,j})$.
 \end{itemize}
 
 
   \end{block}
 
 \begin{block}{Results}
-
+    \begin{center}
+  \includegraphics[scale=1.5]{fig.png}
+  \end{center}
 \end{block}
 
 \begin{block}{References}
-  {\scriptsize \bibliography{../../paper/sparse}
-\bibliographystyle{plain}}
+  {\scriptsize \bibliography{sparse}
+\bibliographystyle{abbrv}}
 \end{block}
 
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