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authorjeanpouget-abadie <jean.pougetabadie@gmail.com>2015-02-05 12:49:11 -0500
committerjeanpouget-abadie <jean.pougetabadie@gmail.com>2015-02-05 12:49:11 -0500
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& \includegraphics[scale=.21]{figures/watts_strogatz.pdf}
& \includegraphics[scale=.23]{figures/kronecker_l2_norm.pdf}
& \includegraphics[scale=.23]{figures/kronecker_l2_norm_nonsparse.pdf}\\
-(a) & (b) & (c) & (d)
+(a) Barabasi-Albert & (b) Watts-Strogatz & (c) sparse Kronecker & (d) non-sparse Kronecker
\end{tabular}
-\captionof{figure}{blabla}
+\captionof{figure}{Figures (a) and (b) report the $f1$-score in $\log$ scale for 2 graphs: (a) Barabasi-Albert graph, $300$ nodes, $16200$ edges. (b) Watts-Strogatz graph, $300$ nodes, $4500$ edges. Figures (c) and (d) report the $\ell2$-norm $\|\hat \Theta - \Theta\|_2$ in the exactly sparse case and the approximately sparse case for a Kronecker graph which is: (c) exactly sparse (d) non-exactly spasre}
\end{table*}
In this section, we validate empirically the results and assumptions of Section~\ref{sec:results} for different initializations of parameters ($n$, $m$, $\lambda$) and for varying levels of sparsity. We compare our algorithm to two different state-of-the-art algorithms: \textsc{greedy} and \textsc{mle} from \cite{Netrapalli:2012}. As an extra benchmark, we also introduce a new algorithm \textsc{lasso}, which approximates our \textsc{sparse mle} algorithm. We find empirically that \textsc{lasso} is highly robust, and can be computed more efficiently than both \textsc{mle} and \textsc{sparse mle} without sacrificing for performance.