From 3bcc519d2fcfdad6c57d50da13e3227fa5f0c13a Mon Sep 17 00:00:00 2001
From: jeanpouget-abadie <jean.pougetabadie@gmail.com>
Date: Thu, 3 Dec 2015 23:14:24 -0500
Subject: adding fig to poster + small typo

---
 poster/Finale_poster/poster.tex | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/poster/Finale_poster/poster.tex b/poster/Finale_poster/poster.tex
index ea94df7..5ec04e4 100644
--- a/poster/Finale_poster/poster.tex
+++ b/poster/Finale_poster/poster.tex
@@ -72,7 +72,7 @@
 \begin{block}{MLE}
   \begin{itemize}
     \item Define for node $j$, $y^t = x^{t+1}_j$
-    \item Observations $\{(x^t, y^t)\}$ are drawn from a GLM. MLE problem:
+    \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_j\cdot x^t)
@@ -122,14 +122,14 @@ i.e.~maximize information gain per observation.
 \vspace{0.5em}
 \textbf{Baseline heuristic:}
 \begin{itemize}
-  \item Choose source w.p. 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}
 
 \vspace{0.5em}
 \textbf{Principled heuristic:}
 \begin{itemize}
-  \item Choose source w.p. proportional to mutual information
+  \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)
@@ -163,13 +163,13 @@ i.e.~maximize information gain per observation.
 
         \textbf{Justification} for any $f$:
         \begin{displaymath}
-            I(X, Y) \geq I\big(f(X)\big)
+            I(X, Y) \geq I\big(f(X), Y\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 $\sum_j \text{Var}(\Theta_{i,j})$.
+      node $i$ w.p.~proportional to $\sum_j \text{Var}(\Theta_{i,j})$.
 \end{itemize}
 
 
@@ -177,7 +177,7 @@ i.e.~maximize information gain per observation.
 
 \begin{block}{Results}
     \begin{center}
-  \includegraphics[scale=1.5]{fig.png}
+  \includegraphics[scale=1.5]{../../simulation/plots/finale.png}
   \end{center}
 \end{block}
 
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