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4 files changed, 591 insertions, 34 deletions
diff --git a/poster/Finale_poster/beamerthemeconfposter.sty b/poster/Finale_poster/beamerthemeconfposter.sty index fc07a08..44acd17 100644 --- a/poster/Finale_poster/beamerthemeconfposter.sty +++ b/poster/Finale_poster/beamerthemeconfposter.sty @@ -99,12 +99,14 @@ \begin{column}{.6\linewidth} \vskip1cm \centering - \usebeamercolor{title in headline}{\color{jblue}\Huge{\textbf{\inserttitle}}\\[0.5ex]} - \usebeamercolor{author in headline}{\color{fg}\Large{\insertauthor}\\[1ex]} + \usebeamercolor{title in headline}{\color{jblue}\huge{\textbf{\inserttitle}}\\[0.5ex]} %\usebeamercolor{institute in headline}{\color{fg}\large{\insertinstitute}\\[1ex]} \end{column} \vspace{1cm} \begin{column}{.2\linewidth} + \begin{center} + \usebeamercolor{author in headline}{\color{fg}\Large{\insertauthor}\\[1ex]} +\end{center} \end{column} \vspace{1cm} \end{columns} diff --git a/poster/Finale_poster/fig.png b/poster/Finale_poster/fig.png Binary files differnew file mode 100644 index 0000000..4d594d4 --- /dev/null +++ b/poster/Finale_poster/fig.png 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} %----------------------------------------------------------------------------- diff --git a/poster/Finale_poster/sparse.bib b/poster/Finale_poster/sparse.bib new file mode 100644 index 0000000..61d57fa --- /dev/null +++ b/poster/Finale_poster/sparse.bib @@ -0,0 +1,541 @@ +@article{pymc, + title={PyMC: Bayesian stochastic modelling in Python}, + author={Patil, Anand and Huard, David and Fonnesbeck, Christopher J}, + journal={Journal of statistical software}, + volume={35}, + number={4}, + pages={1}, + year={2010}, + publisher={Europe PMC Funders} +} + +@article{blocks, + author = {Bart van Merri{\"{e}}nboer and + Dzmitry Bahdanau and + Vincent Dumoulin and + Dmitriy Serdyuk and + David Warde{-}Farley and + Jan Chorowski and + Yoshua Bengio}, + title = {Blocks and Fuel: Frameworks for deep learning}, + journal = {CoRR}, + volume = {abs/1506.00619}, + year = {2015}, + url = {http://arxiv.org/abs/1506.00619}, + timestamp = {Wed, 01 Jul 2015 15:10:24 +0200}, + biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/MerrienboerBDSW15}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article {CandesRomberTao:2006, +author = {Candès, Emmanuel J. and Romberg, Justin K. and Tao, Terence}, +title = {Stable signal recovery from incomplete and inaccurate measurements}, +journal = {Communications on Pure and Applied Mathematics}, +volume = {59}, +number = {8}, +publisher = {Wiley Subscription Services, Inc., A Wiley Company}, +issn = {1097-0312}, +pages = {1207--1223}, +year = {2006}, +} + + +@inproceedings{GomezRodriguez:2010, + author = {Gomez Rodriguez, Manuel and Leskovec, Jure and Krause, Andreas}, + title = {Inferring Networks of Diffusion and Influence}, + booktitle = {Proceedings of the 16th ACM SIGKDD International Conference on + Knowledge Discovery and Data Mining}, + series = {KDD '10}, + year = {2010}, + isbn = {978-1-4503-0055-1}, + location = {Washington, DC, USA}, + pages = {1019--1028}, + numpages = {10}, + publisher = {ACM}, + address = {New York, NY, USA}, +} + +@inproceedings{Pouget:2015, + title={Inferring graphs from cascades: A Sparse Recovery Framework}, + author={Pouget-Abadie, Jean and Horel, Thibaut}, + series={ICML'15}, + year={2015} +} + +@inproceedings{du2013uncover, + title={Uncover topic-sensitive information diffusion networks}, + author={Du, Nan and Song, Le and Woo, Hyenkyun and Zha, Hongyuan}, + booktitle={Proceedings of the Sixteenth International Conference on + Artificial Intelligence and Statistics}, + pages={229--237}, + year={2013} +} + +@inproceedings{du2014influence, + title={Influence function learning in information diffusion networks}, + author={Du, Nan and Liang, Yingyu and Balcan, Maria and Song, Le}, + booktitle={Proceedings of the 31st International Conference on Machine + Learning (ICML-14)}, + pages={2016--2024}, + year={2014} +} + + +@article{Netrapalli:2012, + author = {Netrapalli, Praneeth and Sanghavi, Sujay}, + title = {Learning the Graph of Epidemic Cascades}, + journal = {SIGMETRICS Perform. 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