From 5f82a47d7ad642b05d089ca43811aba3a233b224 Mon Sep 17 00:00:00 2001
From: jeanpouget-abadie <jean.pougetabadie@gmail.com>
Date: Thu, 3 Dec 2015 11:51:40 -0500
Subject: poster

---
 poster/Finale_poster/poster.tex | 33 ++++++++++++++++++++++++---------
 1 file changed, 24 insertions(+), 9 deletions(-)

(limited to 'poster/Finale_poster/poster.tex')

diff --git a/poster/Finale_poster/poster.tex b/poster/Finale_poster/poster.tex
index 7cc14b8..63219a7 100644
--- a/poster/Finale_poster/poster.tex
+++ b/poster/Finale_poster/poster.tex
@@ -1,4 +1,4 @@
-\documentclass[final]{beamer}
+\documentclass[final, 10]{beamer}
 \usepackage[utf8]{inputenc}
 \usepackage[scale=1.6]{beamerposter} % Use the beamerposter package for laying
 \usetheme{confposter} % Use the confposter theme supplied with this template
@@ -63,28 +63,43 @@
 \begin{block}{Problem}
   \emph{How to recover an unknown network from the observation of contagion
   cascades?}
+  \vspace{.5cm}
+  \begin{itemize}
+  \item {\bf Observe} $X^t_c$ (infections at time $t$ in cascade $c$)
+  \item {\bf Objective}: find $\{\theta_{ij}\}$ (graph weight matrix)
+\end{itemize}
 \end{block}
 \vspace{1cm}
 
 \begin{block}{\bf Contagion Model~\cite{}}
 \begin{itemize}
-  \item {\bf Observe} $X^t_c$ (infections at time $t$ in cascade $c$)
-  \item {\bf Objective}: find $\{\theta_{ij}\}$ (graph weight matrix)
-  \item Infections drawn indep.~for each node: GLM over infected parents
+  \item Discrete time
+  \item Infections drawn indep.~for each node conditioned on previous step
+  \item Generalized Linear Model parametrization:
     \begin{framed}
     $$\mathbb{P}(X^{t+1}_j = 1 | X^t) = f(\Theta_j \cdot X^t)$$
     \end{framed}
 \end{itemize}
-\begin{figure}
-  \centering
-  \includegraphics[scale=1.5]{../images/drawing.pdf}
-\end{figure}
+\end{block}
+
+\begin{block}{MLE}
+  \begin{itemize}
+    \item Log-likelihood is concave for common contagion models (IC model): SGD
+      on $\{\theta_{ij}\}$
+  \end{itemize}
+  \vspace{1cm}
+  \begin{equation*}
+    \begin{split}
+      \hat{\theta}\in \arg\max_\theta \sum_{t}~& y^t\log f(\theta\cdot x^t)
+      \\ & + (1-y^t) \log \big(1 - f(\theta\cdot x^t)\big)
+  \end{split}
+\end{equation*}
 \end{block}
 
 \begin{block}{Bayesian Framework}
 \begin{figure}
   \centering
-  \includegraphics[scale=1.5]{graphical.pdf}
+  \includegraphics[scale=3]{graphical.pdf}
 \end{figure}
 \end{block}
 
-- 
cgit v1.2.3-70-g09d2

