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| -rw-r--r-- | paper/sections/experiments.tex | 5 |
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diff --git a/paper/sections/experiments.tex b/paper/sections/experiments.tex index a4fd1e9..3891526 100644 --- a/paper/sections/experiments.tex +++ b/paper/sections/experiments.tex @@ -13,7 +13,8 @@ & \includegraphics[scale=.23]{figures/kronecker_l2_norm_nonsparse.pdf}\\ (a) Barabasi-Albert & (b) Watts-Strogatz & (c) sparse Kronecker & (d) non-sparse Kronecker \end{tabular} -\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} +\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 $\|\hat \Theta - \Theta\|_2$ for a Kronecker graph which is: (c) exactly sparse (d) non-exactly sparse} +\label{fig:four_figs} \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. @@ -38,4 +39,4 @@ This algorithm, which we name \textsc{Lasso}, has the merit of being both easier \paragraph{Quantifying robustness} -The previous experiments only considered graphs with strong edges. To test the algorithms in the approximately sparse case, we add sparse edges to the previous graphs according to a bernoulli variable of parameter $1/3$ for every non-edge, and drawing a weight uniformly from $[0,0.1]$. The results are reported in Figure XXX by plotting the convergence of the $\ell2$-norm error, and show that both the \textsc{lasso}, followed by \textsc{sparse mle} are the most robust to noise.
\ No newline at end of file +The previous experiments only considered graphs with strong edges. To test the algorithms in the approximately sparse case, we add sparse edges to the previous graphs according to a bernoulli variable of parameter $1/3$ for every non-edge, and drawing a weight uniformly from $[0,0.1]$. The results are reported in Figure~\ref{fig:four_figs} by plotting the convergence of the $\ell2$-norm error, and show that both the \textsc{lasso}, followed by \textsc{sparse mle} are the most robust to noise.
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