diff options
| -rw-r--r-- | poster/Finale_poster/beamerthemeconfposter.sty | 12 | ||||
| -rw-r--r-- | poster/Finale_poster/poster.tex | 110 |
2 files changed, 68 insertions, 54 deletions
diff --git a/poster/Finale_poster/beamerthemeconfposter.sty b/poster/Finale_poster/beamerthemeconfposter.sty index 9d04bf8..fc07a08 100644 --- a/poster/Finale_poster/beamerthemeconfposter.sty +++ b/poster/Finale_poster/beamerthemeconfposter.sty @@ -1,7 +1,7 @@ %============================================================================== % Beamer style for the poster template posted at % www.nathanieljohnston.com/index.php/2009/08/latex-poster-template -% +% % Created by the Computational Physics and Biophysics Group at Jacobs University % https://teamwork.jacobs-university.de:8443/confluence/display/CoPandBiG/LaTeX+Poster % Modified by Nathaniel Johnston (nathaniel@nathanieljohnston.com) in August 2009 @@ -78,7 +78,7 @@ \setbeamercolor{bibliography item}{fg=black,bg=white} \setbeamercolor{bibliography entry author}{fg=black,bg=white} \setbeamercolor{bibliography item}{fg=black,bg=white} - + % define some length variables that are used by the template \newlength{\inboxwd} \newlength{\iinboxwd} @@ -135,10 +135,10 @@ \usebeamerfont{block body} \vskip-0.5cm \begin{beamercolorbox}[colsep*=0ex,vmode]{block body} - \justifying + \justifying } -\setbeamertemplate{block end} +\setbeamertemplate{block end} { \end{beamercolorbox} \vskip\smallskipamount @@ -165,10 +165,10 @@ \addtolength{\inboxrule}{0.5cm} \begin{center} \begin{minipage}{\iinboxwd} - \justifying + \justifying } -\setbeamertemplate{block alerted end} +\setbeamertemplate{block alerted end} { \end{minipage} \end{center} diff --git a/poster/Finale_poster/poster.tex b/poster/Finale_poster/poster.tex index c750194..8f1bd1d 100644 --- a/poster/Finale_poster/poster.tex +++ b/poster/Finale_poster/poster.tex @@ -63,16 +63,16 @@ \vspace{1em} \begin{figure} \begin{center} - \includegraphics[scale=1.5]{drawing.pdf} + \includegraphics[scale=2.5]{drawing.pdf} \end{center} \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} + \item For node $i$, $y^t = x^{t+1}_i$ + \item For node $i$, $\{(x^t, y^t)\}$ are drawn from a GLM + \item SGD on $\{\theta_{ij}\}$ \vspace{1cm} \begin{equation*} \begin{split} @@ -80,68 +80,58 @@ \\ & + (1-y^t) \log \big(1 - f(\theta\cdot x^t)\big) \end{split} \end{equation*} +\item Log-likelihood is concave for common contagion models (IC model) +\item Prior work~\cite{} finds convergence guarantees for $L1$-regularization + \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}{Bayesian Framework} \begin{figure} \centering \includegraphics[scale=3]{graphical.pdf} \end{figure} +{\bf Advantages:} \begin{itemize} - \item $\phi$: fixed source distribution - \item capture uncertainty on each edge - \item encode expressive graph priors (tied parameters) + \item encode expressive graph priors (e.g. ERGMs) + \item quantify uncertainty over each edge +\end{itemize} +{\bf Disadvantages:} +\begin{itemize} + \item Hard to scale in large data volume regime \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}{Active Learning} \emph{Can we gain by choosing the source node? If so, how to best choose the source node?} + \begin{center}--OR--\end{center} + \emph{Can we choose the parts of the dataset we compute next?} \end{block} -\begin{block}{Heuristic 1} - \begin{itemize} - \item Choose source proportional to estimated degree - \item Intuition: - \begin{itemize} - \item deeper cascades $\implies$ more data - \item easier to learn non-edges than edges. Higher degree $\implies$ - more edge realizations at the same price. - \end{itemize} - \end{itemize} -\end{block} +{\bf Idea:} Focus on parts of the graph which are unexplored (high uncertainty). +i.e.~maximize information gain per cascade -\begin{block}{Heuristic 2} - \begin{itemize} - \item Choose source proportional to mutual information +Baseline heuristic: +\begin{itemize} + \item Choose source proportional to estimated out-degree $\implies$ wider + cascades $\implies$ more data +\end{itemize} + +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 Exact strategy requires knowing true distribution of $(X_t)$ + \item Use estimated $\Theta$ to compute $H(\Theta | (X_t), X_0 = i)$ \end{itemize} -\end{block} - -\begin{block}{Heuristic 3} - \begin{itemize} - \item Choose source proportional to mutual information of first step of - cascade and $\Theta$: - \item Intuition: - \begin{itemize} - \item Choose lower bound of mutual information $I(X, Y) \geq I(f(X), - g(Y))$ - \item First step is most informative~\cite{} - \end{itemize} - \end{itemize} -\end{block} - \end{column} %----------------------------------------------------------------------------- \begin{column}{\sepwid}\end{column} @@ -149,9 +139,33 @@ \begin{column}{\onecolwid} % The third column -%----------------------------------------------------------------------------- -% REFERENCES -%----------------------------------------------------------------------------- + \begin{block}{Implementation} + {\bf Scalable Bayesian Inference} + \begin{itemize} + \item MCMC (PyMC~\cite{}) + \item VI (BLOCKS~\cite{}) + \end{itemize} + + {\bf Scalable Active Learning Criterion} +Approx.~heuristic: +\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 +\end{itemize} + + + \end{block} + +\begin{block}{Results} + +\end{block} \begin{block}{References} {\scriptsize \bibliography{../../paper/sparse} |