small changes

2 files changed, 30 insertions, 2 deletions

diff --git a/paper/sections/experiments.tex b/paper/sections/experiments.tex
index e2cc2e1..a4fd1e9 100644
--- a/paper/sections/experiments.tex
+++ b/paper/sections/experiments.tex
@@ -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.
 
diff --git a/paper/sparse.bib b/paper/sparse.bib
index 48017cc..6cebf03 100644
--- a/paper/sparse.bib
+++ b/paper/sparse.bib
@@ -371,3 +371,32 @@ year = "2009"
   pages = {026--107},
   year = {2002}
 }
+
+
+@article{watts:1998,
+  Annote = {10.1038/30918},
+  Author = {Watts, Duncan J. and Strogatz, Steven H.},
+  Date = {1998/06/04/print},
+  Isbn = {0028-0836},
+  Journal = {Nature},
+  Number = {6684},
+  Pages = {440--442},
+  Read = {0},
+  Title = {Collective dynamics of `small-world' networks},
+  Url = {http://dx.doi.org/10.1038/30918},
+  Volume = {393},
+  Year = {1998},
+}
+
+@article{barabasi:2001,
+  author    = {R{\'{e}}ka Albert and
+               Albert{-}L{\'{a}}szl{\'{o}} Barab{\'{a}}si},
+  title     = {Statistical mechanics of complex networks},
+  journal   = {CoRR},
+  volume    = {cond-mat/0106096},
+  year      = {2001},
+  url       = {http://arxiv.org/abs/cond-mat/0106096},
+  timestamp = {Mon, 05 Dec 2011 18:05:15 +0100},
+  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/corr/cond-mat-0106096},
+  bibsource = {dblp computer science bibliography, http://dblp.org}
+}