From c6892e3c7988e2b7b2f11435cf689711bc495f0b Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Sun, 15 Mar 2015 14:32:05 -0400
Subject: Experiments

---
 poster_abstract/main.tex | 24 +++++++++++++++++++++++-
 1 file changed, 23 insertions(+), 1 deletion(-)

(limited to 'poster_abstract/main.tex')

diff --git a/poster_abstract/main.tex b/poster_abstract/main.tex
index d3ce670..41c074f 100644
--- a/poster_abstract/main.tex
+++ b/poster_abstract/main.tex
@@ -234,10 +234,32 @@ process (cascades) are observed.
 
 \section{Experiments}
 
+We compared the performance of Algorithm~\eqref{eq:pre-mle} to prior algorithms
+for the Graph Inference problem. Given our estimate $\tilde{\Theta}$ of the
+edge weights, we recover the edges of the graph by simple thresholding: $E
+= \cup_{j \in V} \{(i,j) : \tilde{\Theta}_{ij} > \eta\}$, for varying values
+of $\eta$. We used the F1-score as a measure of performance: $\text{F1}=2
+\text{precision}\cdot\text{recall}/(\text{precision}+\text{recall})$.
+
+The algorithms were tested on several synthetic networks generated from
+standard social networks model. The results are shown in Figure~\ref{fig:exp}
+for the Watts-Strogatz model. The full version of the paper contains more
+comprehensive experiments.
+
+% which
+% considers \emph{(1)} the number of true edges recovered by the algorithm over
+% the total number of edges returned by the algorithm (\emph{precision}) and
+% \emph{(2)} the number of true edges recovered by the algorithm over the total
+% number of edges it should have recovered (\emph{recall}).
+
 \begin{figure}
+    \label{fig:exp}
 \centering
 \includegraphics[scale=.35]{../paper/figures/watts_strogatz.pdf}
-\caption{F1 score as a function of the number of observed cascades for a Watts-Strogatz graph, for the Greedy and MLE algorithm from \cite{Netrapalli:2012}, a Lasso algorithm which approximates \label{eq:pre-mle}, and the penalized log-likelihood program.}
+\caption{F1 score as a function of the number of observed cascades for
+a Watts-Strogatz graph, for the Greedy and MLE algorithm from
+\cite{Netrapalli:2012}, a Lasso algorithm which approximates \eqref{eq:pre-mle},
+and the penalized log-likelihood program \eqref{eq:pre-mle}.}
 \end{figure}
 %\section{Acknowledgments}
 
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