From 393cba417046147286001e7317a36db148545bb1 Mon Sep 17 00:00:00 2001
From: jeanpouget-abadie <jean.pougetabadie@gmail.com>
Date: Wed, 4 Feb 2015 18:39:03 -0500
Subject: routine commit

---
 paper/sections/experiments.tex | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

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diff --git a/paper/sections/experiments.tex b/paper/sections/experiments.tex
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@@ -8,6 +8,25 @@
 \caption{Watts-Strogatz Model. 200 nodes, 20000 edges.}
 \end{figure}
 
+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}. We introduce an approximate \textsc{Lasso} algorithm and validate its effectiveness empirically.
+
+\paragraph{Experimental setup}
+
+We focus our analysis to synthetic graphs, which are known to exhibit the properties of real social networks. We therefore consider a Watts-Strogatz graph ($300$ nodes, $4500$ edges), a Barabasi-Albert graph ($300$ nodes, $16200$ edges), the 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}. For every reported data point, we generate $n$ cascades from the Independent Cascade model for $n \in \{100, 500, 1000, 2000, 5000\}$, and compute the estimated graph $\hat {\cal G}$ for each algorithm. 
+
+In the case of the \textsc{Lasso}, \textsc{MLE} and \textsc{Sparse MLE} algorithms, we construct the edges of $\hat {\cal G} : \cup_{j \in V} \{i : \Theta_{ij} > 0.1\}$. We report the F1-score$=2\frac{\text{precision}\cdot\text{recall}}{\text{precision}+\text{recall}}$. For each graph, 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.  Except when testing for approximately sparse graphs, all edge weights are chosen uniformly in the interval $[0.2, 0.7]$.
+
+\paragraph{Comparison with other algorithms}
+\begin{itemize}
+\item Continuous time + single source -> no comparison with NETRATE...
+\item This is a modeling decision: in practice, we do not have access to the cascade's ``patient 0'', which makes learning the graph harder.
+\item Lasso
+\end{itemize}
+
+
+\paragraph{Quantifying robustness}
+
+
 
 \begin{itemize}
 \item Compare edge recovery to First Edge and Greedy as number of cascades grows on different types of graphs...
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