From b2e37a91f5ae65a003bb528812a79d6800908de6 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Thu, 3 Dec 2015 18:44:11 -0500
Subject: Polishing the first 1.5 column

---
 poster/Finale_poster/poster.tex | 32 ++++++++++++++++----------------
 1 file changed, 16 insertions(+), 16 deletions(-)

diff --git a/poster/Finale_poster/poster.tex b/poster/Finale_poster/poster.tex
index 8f1bd1d..1365801 100644
--- a/poster/Finale_poster/poster.tex
+++ b/poster/Finale_poster/poster.tex
@@ -70,18 +70,18 @@
 
 \begin{block}{MLE}
   \begin{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}
+    \item Define for node $j$, $y^t = x^{t+1}_j$
+    \item Observations $\{(x^t, y^t)\}$ are drawn from a GLM. MLE problem:
   \begin{equation*}
     \begin{split}
-      \hat{\theta}\in \arg\max_\theta \sum_{t}~& y^t\log f(\theta\cdot x^t)
-      \\ & + (1-y^t) \log \big(1 - f(\theta\cdot x^t)\big)
+      \hat{\theta}\in \arg\max_\theta \sum_{t}~& y^t\log f(\Theta_j\cdot x^t)
+      \\ & + (1-y^t) \log \big(1 - f(\Theta_j\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
+    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{}).
   \end{itemize}
 \end{block}
 \end{column} % End of the first column
@@ -98,21 +98,20 @@
 \end{figure}
 {\bf Advantages:}
 \begin{itemize}
-  \item encode expressive graph priors (e.g. ERGMs)
-  \item quantify uncertainty over each edge
+  \item prior encodes domain-specific knowledge of graph structure (e.g. ERGMs)
+  \item posterior expresses uncertainty over edge weights
 \end{itemize}
 {\bf Disadvantages:}
 \begin{itemize}
-  \item Hard to scale in large data volume regime
+  \item hard to scale when large number of observations.
 \end{itemize}
 \end{block}
 
 \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}
+  \emph{Can we learn faster by choosing the source node? If so, how to best
+  choose it?}
+  \begin{center}--~OR~--\end{center}
+  \emph{Can we cherry-pick the most relevant part of the dataset?}
 
 {\bf Idea:} Focus on parts of the graph which are unexplored (high uncertainty).
 i.e.~maximize information gain per cascade
@@ -132,6 +131,7 @@ Principled heuristic:
   \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}
 \end{column}
 %-----------------------------------------------------------------------------
 \begin{column}{\sepwid}\end{column}
-- 
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