From c6892e3c7988e2b7b2f11435cf689711bc495f0b Mon Sep 17 00:00:00 2001 From: Thibaut Horel 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') 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} -- cgit v1.2.3-70-g09d2