finished first pass

1 files changed, 62 insertions, 48 deletions

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}