Experiments

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--- a/poster_abstract/main.tex
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@@ -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}