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+\documentclass[final]{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
+
+\usepackage{framed, amsmath, amsthm, amssymb}
+\usepackage{color, bbm}
+\setbeamercolor{block title}{fg=dblue,bg=white} % Colors of the block titles
+\setbeamercolor{block body}{fg=black,bg=white} % Colors of the body of blocks
+\setbeamercolor{block alerted title}{fg=white,bg=dblue!70} % Colors of the
+\setbeamercolor{block alerted body}{fg=black,bg=dblue!10} % Colors of the body
+
+\newlength{\sepwid}
+\newlength{\onecolwid}
+\newlength{\twocolwid}
+\newlength{\threecolwid}
+\setlength{\paperwidth}{48in} % A0 width: 46.8in
+\setlength{\paperheight}{40in} % A0 height: 33.1in
+\setlength{\sepwid}{0.024\paperwidth} % Separation width (white space) between
+\setlength{\onecolwid}{0.22\paperwidth} % Width of one column
+\setlength{\twocolwid}{0.464\paperwidth} % Width of two columns
+\setlength{\threecolwid}{0.708\paperwidth} % Width of three columns
+\setlength{\topmargin}{-1in} % Reduce the top margin size
+%-----------------------------------------------------------
+
+\usepackage{graphicx}
+\usepackage{booktabs}
+
+%----------------------------------------------------------------------------------------
+%	TITLE SECTION
+%----------------------------------------------------------------------------------------
+
+\title{Inferring Graphs from Cascades} % Poster title
+
+\author{Jean Pouget-Abadie, Thibaut Horel} % Author(s)
+
+\institute{Harvard University} % Institution(s)
+%----------------------------------------------------------------------------------------
+\begin{document}
+\addtobeamertemplate{block end}{}{\vspace*{2ex}} % White space under blocks
+\addtobeamertemplate{block alerted end}{}{\vspace*{2ex}} % White space under
+
+\setlength{\belowcaptionskip}{2ex} % White space under figures
+\setlength\belowdisplayshortskip{2ex} % White space under equations
+
+\begin{frame}[t]
+\begin{columns}[t]
+\begin{column}{\sepwid}\end{column}
+\begin{column}{\onecolwid} % The first column
+
+%----------------------------------------------------------------------------------------
+%	INTODUCTION
+%----------------------------------------------------------------------------------------
+
+
+\vspace{- 12.2 cm}
+\begin{center}
+{\includegraphics[scale=2.5]{../images/SEASLogo_RGB.png}}
+\end{center}
+
+\vspace{5 cm}
+
+\begin{block}{Problem Statement}
+
+\begin{itemize}
+  \item A {\bf diffusion process} describes the evolution of a behavior, which
+    is transmitted from node to node along the edges of a network.
+  \item If the network is {\bf unknown} and only the behaviors of nodes in time
+    is observed, for which diffusion processes can we recover the edges?  In
+    how many measurements?
+\end{itemize}
+
+{\bf Notation}
+\begin{itemize}
+  \item $X^t_c \in {\{0,1\}}^n$ set of infected nodes at time $t$ in cascade $c$
+  \item $p_{i,j}$: weight of directed edge $i\rightarrow j$
+\end{itemize}
+
+{\bf Objective}
+\begin{itemize}
+  \item We observe $(c, t, X^t_c)$
+  \item Find $\hat p$ such that $\|p - \hat p\|_2 \leq \epsilon$
+\end{itemize}
+
+\end{block}
+
+\begin{block}{Independent Cascade Model~\cite{Kempe:03}}
+
+\begin{figure}
+\centering
+\includegraphics[width=0.6\textwidth]{../images/voter.png}
+\end{figure}
+
+\begin{itemize}
+  \item Probability that $j^{th}$ node gets infected:
+    \begin{framed}
+      \begin{align*}
+        \tag{IC}
+        \mathbb{P}\big[X^{t+1}_j  = 1\,|\, X^{t}\big]
+            & = 1 - \prod_{i = 1}^m {(1 - p_{i,j})}^{X^t_i} \\
+            & = 1 - \prod_{i = 1}^m e^{\Theta_{i,j}X^t_i} \\
+            & = 1 - e^{\Theta_j \cdot X^t}
+      \end{align*}
+  \end{framed}
+      where $\Theta_{i,j} \equiv \log(1- p_{i,j})$
+\end{itemize}
+
+\end{block}
+
+\end{column} % End of the first column
+
+%-----------------------------------------------------------------------------
+\begin{column}{\sepwid}\end{column} % Empty spacer column
+%-----------------------------------------------------------------------------
+\begin{column}{\onecolwid} % The first column
+
+\begin{block}{Voter Model}
+\begin{figure}
+\centering
+\includegraphics[width=0.6\textwidth]{../images/icc.png}
+\end{figure}
+
+\begin{itemize}
+  \item Probability that $j^{th}$ node gets infected:
+    \begin{framed}
+      \begin{equation*}
+        \tag{VT}
+      \mathbb{P}\big[X^{t+1}_j = 1\,|\, X^{t}\big]
+    = \sum_{i \in X^t} p_{i,j} = p_j \cdot X^t
+      \end{equation*}
+  \end{framed}
+\end{itemize}
+
+\end{block}
+
+
+\begin{block}{Reformulation}
+
+{\bf Generalized Linear Cascade Model}
+\begin{itemize}
+  \item $f: \mathbb{R} \rightarrow [0,1]$: inverse link function
+  \item Probability depends on $f$-transform of scalar product:
+    \begin{framed}
+    $$\mathbb{P}(X^{t+1}_j = 1 | X^t) = f(\Theta_j \cdot X^t)$$
+    \end{framed}
+\end{itemize}
+
+{\bf Setup}
+\begin{figure}
+  \centering
+  \includegraphics[scale=1.5]{../images/drawing.pdf}
+\end{figure}
+
+{\bf Examples:}
+\begin{itemize}
+  \item Independent Cascade (IC) Model: $f : z \mapsto 1-e^z$
+  \item Voter model: $f : z \mapsto z$
+  \item Discrete-version of continuous IC model~\cite{GomezRodriguez:2010}
+  \item Logistic cascades: $f: z\mapsto \frac{1}{1-e^z}$
+\end{itemize}
+
+\end{block}
+\end{column}
+%-----------------------------------------------------------------------------
+\begin{column}{\sepwid}\end{column}
+%-----------------------------------------------------------------------------
+
+\begin{column}{\onecolwid}
+
+\begin{block}{Sparse Recovery}
+
+\begin{itemize}
+  \item Solving for $A x = b$ when $A$ is non-degenerate is possible if
+      \begin{itemize}
+        \item $A$ is {\bf almost invertible}
+        \item $x$ is {\bf sparse}
+      \end{itemize}
+  \item If $x$ is solution to $\min L(x)$ where
+    $L$ is convex, then~\cite{Negahban:2009}~solve for:
+    \begin{equation*}
+      \min_x L(x) + \lambda \| x\|
+    \end{equation*}
+\end{itemize}
+\end{block}
+
+\begin{theorem}
+    {\bf Assumptions}:
+    \begin{itemize}
+        \item $f$ and $1-f$ are log-concave with log-gradient bounded by
+          $\frac{1}{\alpha}$
+      \item $\nabla^2 {\cal L}$ verifies the $(S,\gamma)$-{\bf
+    RE} condition
+    \vspace{1cm}
+\end{itemize} {\bf Algorithm}:
+    \begin{itemize}
+      \item Solve MLE program with $\lambda = 2\sqrt{\frac{\log m}{\alpha n}}$
+        \begin{framed}
+        \begin{equation*}
+          \hat \theta_i \in \arg \max_{\theta} {\cal L}_i(\theta_i | x^1,
+          \dots x^n) - \lambda \|\theta_i\|_1
+        \end{equation*}
+      \end{framed}
+    \end{itemize}
+    \vspace{1cm}
+    {\bf Guarantee}
+      With high probability:
+    \begin{framed}
+    \begin{equation*}
+    \|\hat \theta - \theta^*\|_2 \leq \frac{6}{\gamma} \sqrt{\frac{s \log
+      m}{\alpha n}}
+    \end{equation*}
+  \end{framed}
+    where $s$ is degree of node, $m$ is number of nodes, $n$ is the number of
+    observations
+\end{theorem}
+
+\begin{block}{Restricted Eigenvalue Condition}
+  {\bf Definition}
+  \begin{itemize}
+    \item $C(S) \equiv \{ X :\|X_{\bar S}\|_1 \leq 3 \|X\|_1\}$
+    \item Matrix $A$ verifies the $(\gamma, S)$-{(\bf RE)} condition if:
+      $$\forall X \in C({\cal S}), X^T A X \geq \gamma \|X\|_2^2$$
+  \end{itemize}
+
+   \vspace{1cm}
+  {\bf Hessian $\mapsto$ Gram Matrix}
+  \begin{itemize}
+    \item If $f$ and $1-f$ are $c$-strictly log-convex, we can replace the
+      condition on the $\nabla^2 {\cal L}$ by the same condition on the Gram
+      matrix $X^T X$.
+  \end{itemize}
+    \vspace{1cm}
+  {\bf Hessian $\mapsto$ Expected Hessian}
+  \begin{itemize}
+    \item If $\mathbb{E}[A]$ verifies the $(S, \gamma)$-{(\bf RE)} condition,
+      then $A$ verifies the $(S, \gamma/2)$-{(\bf RE)}
+     condition~\cite{vandegeer:2009}
+  \end{itemize}
+
+\end{block}
+
+\end{column} % End of the second column
+
+%-----------------------------------------------------------------------------
+\begin{column}{\sepwid}\end{column} % Empty spacer column
+%-----------------------------------------------------------------------------
+\begin{column}{\onecolwid} % The third column
+  \begin{block}{Experimental validation}
+    \begin{figure}
+      \centering
+      \includegraphics[scale=1.2]{../images/watts_strogatz.pdf}
+    \caption{Watts-Strogatz, $300$ nodes, $4500$ edges, uniform edge weights,
+    constant $p_{init}$}
+    \end{figure}
+  \end{block}
+
+
+\begin{block}{Conclusion}
+  \begin{itemize}
+    \item Introduce Generalized Linear Casacade model
+    \item Better finite sample guarantees~\cite{Netrapalli:2012, Abrahao:13,
+        Daneshmand:2014}
+    \item Interpretable conditions on Hessian
+    \item Lower bound+approximately sparse case developed in full
+      paper~\cite{Pouget:2015}
+  \end{itemize}
+\end{block}
+
+%-----------------------------------------------------------------------------
+%	REFERENCES
+%-----------------------------------------------------------------------------
+
+\begin{block}{References}
+  {\scriptsize
+  \bibliography{../../paper/sparse}
+\bibliographystyle{plain}}
+\end{block}
+
+%-----------------------------------------------------------------------------
+
+\end{column} % End of the third column
+
+\end{columns} % End of all the columns in the poster
+
+\end{frame} % End of the enclosing frame
+
+
+
+\end{document}