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-rw-r--r--poster/Finale_poster/poster.tex12
1 files 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}