%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%% ICML 2015 EXAMPLE LATEX SUBMISSION FILE %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Use the following line _only_ if you're still using LaTeX 2.09.
%\documentstyle[icml2015,epsf,natbib]{article}
% If you rely on Latex2e packages, like most moden people use this:
\documentclass{article}

% use Times
\usepackage{times}
% For figures
\usepackage{graphicx} % more modern
%\usepackage{epsfig} % less modern
\usepackage{subfigure}

% For citations
\usepackage{natbib}

% For algorithms
\usepackage{algorithm}
\usepackage{algorithmic}

% As of 2011, we use the hyperref package to produce hyperlinks in the
% resulting PDF.  If this breaks your system, please commend out the
% following usepackage line and replace \usepackage{icml2015} with
% \usepackage[nohyperref]{icml2015} above.
\usepackage{hyperref}

% Packages hyperref and algorithmic misbehave sometimes.  We can fix
% this with the following command.
\newcommand{\theHalgorithm}{\arabic{algorithm}}

% Employ the following version of the ``usepackage'' statement for
% submitting the draft version of the paper for review.  This will set
% the note in the first column to ``Under review.  Do not distribute.''
\usepackage[accepted]{icml2015}

% Employ this version of the ``usepackage'' statement after the paper has
% been accepted, when creating the final version.  This will set the
% note in the first column to ``Proceedings of the...''
%\usepackage[accepted]{icml2015}
\usepackage[utf8]{inputenc}
\usepackage{caption}
\usepackage{array}

% This is only temporary to take the reviewers' comments into account
\usepackage{color}
% The \icmltitle you define below is probably too long as a header.
% Therefore, a short form for the running title is supplied here:
\icmltitlerunning{Inferring Graphs from Cascades: A Sparse Recovery Framework}

\usepackage{amsmath, amsfonts, amssymb, amsthm, bbm}
\usepackage{verbatim}
\newcommand{\reals}{\mathbb{R}}
\newcommand{\ints}{\mathbb{N}}
\renewcommand{\O}{\mathcal{O}}
\DeclareMathOperator{\E}{\mathbb{E}}
\let\P\relax
\DeclareMathOperator{\P}{\mathbb{P}}
\newcommand{\ex}[1]{\E\left[#1\right]}
\newcommand{\prob}[1]{\P\left[#1\right]}
\newcommand{\inprod}[2]{#1 \cdot #2}
\newcommand{\defeq}{\equiv}
\DeclareMathOperator*{\argmax}{argmax}
\DeclareMathOperator*{\argmin}{argmin}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{corollary}{Corollary}
\newtheorem{remark}{Remark}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{fact}{Fact}

\begin{document}

\twocolumn[
\icmltitle{Inferring Graphs from Cascades: A Sparse Recovery Framework}

% It is OKAY to include author information, even for blind
% submissions: the style file will automatically remove it for you
% unless you've provided the [accepted] option to the icml2015
% package.
\icmlauthor{Jean Pouget-Abadie}{jeanpougetabadie@g.harvard.edu}
\icmladdress{Harvard University}
\icmlauthor{Thibaut Horel}{thorel@seas.harvard.edu}
\icmladdress{Harvard University}

% You may provide any keywords that you
% find helpful for describing your paper; these are used to populate
% the "keywords" metadata in the PDF but will not be shown in the document
\icmlkeywords{Sparse Recovery, Cascade Models, Graph Inference, Networks,
Diffusion Processes}

\vskip 0.3in
]

\begin{abstract}
\input{sections/abstract.tex}
\end{abstract}

\section{Introduction}
\input{sections/intro.tex}

\section{Model}
\label{sec:model}
\input{sections/model.tex}

\section{Results}
\label{sec:results}
\input{sections/results.tex}

\section{A Lower Bound}
\label{sec:lowerbound}
\input{sections/lowerbound.tex}

\section{Experiments}
\label{sec:experiments}
\input{sections/experiments.tex}

\section{Future Work}
\label{sec:linear_threshold}
\input{sections/discussion.tex}

\newpage

\section*{Acknowledgments}

We would like to thank Yaron Singer, David Parkes, Jelani Nelson, Edoardo
Airoldi and Or Sheffet for helpful discussions. We are also grateful to the
anonymous reviewers for their insightful feedback and suggestions.
\bibliography{sparse}
\bibliographystyle{icml2015}

\newpage
\section{Appendix}
\input{sections/appendix.tex}

\end{document}
