From 74c76d367d4e2d92b235a0f00f2134a33787b987 Mon Sep 17 00:00:00 2001
From: jeanpouget-abadie <jean.pougetabadie@gmail.com>
Date: Thu, 5 Feb 2015 13:49:53 -0500
Subject: small changes

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 paper/sections/experiments.tex | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

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diff --git a/paper/sections/experiments.tex b/paper/sections/experiments.tex
index e2cc2e1..a4fd1e9 100644
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@@ -19,8 +19,7 @@
 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.
 
 \paragraph{Experimental setup}
-
-We evaluate the performance of the algorithms on synthetic graphs, chosen for their similarity to real social networks. We therefore consider a Watts-Strogatz graph ($300$ nodes, $4500$ edges), a Barabasi-Albert graph ($300$ nodes, $16200$ edges), a Holme-Kim power law graph ($200$ nodes, $9772$ edges) \cite{Holme:2002}, and the recently introduced Kronecker graph ($256$ nodes, $10000$ edges) \cite{Leskovec:2010}. Undirected graphs are converted to directed graphs by doubling the edges.
+We evaluate the performance of the algorithms on synthetic graphs, chosen for their similarity to real social networks. We therefore consider a Watts-Strogatz graph ($300$ nodes, $4500$ edges) \cite{watts:1998}, a Barabasi-Albert graph ($300$ nodes, $16200$ edges) \cite{barabasi:2001}, a Holme-Kim power law graph ($200$ nodes, $9772$ edges) \cite{Holme:2002}, and the recently introduced Kronecker graph ($256$ nodes, $10000$ edges) \cite{Leskovec:2010}. Undirected graphs are converted to directed graphs by doubling the edges.
 
 For every reported data point, we generate $n$ cascades from the Independent Cascade model for $n \in \{100, 500, 1000, 2000, 5000\}$, and compare for each algorithm the estimated graph $\hat {\cal G}$ with ${\cal G}$. The initial probability of a node being a source is fixed to $0.05$, i.e. an average of $15$ nodes source nodes per cascades for all experiments. All edge weights are chosen uniformly in the interval $[0.2, 0.7]$, except when testing for approximately sparse graphs (see paragraph on robustness). All data points are reported with a $\pm 1$ error margin.
 
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