abstract

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 In the Graph Inference problem, one seeks to recover the edges of an unknown
-graph from the observations of influence cascades propagating over this graph.
-In this paper, we approach this problem from the sparse recovery perspective
-and provide the first algorithm which recovers the graph's edges with high
-probability provided that the number of measurements is $\Omega(s\log m)$ where
+graph from the observations of cascades propagating over this graph.
+In this paper, we approach this problem from the sparse recovery perspective.
+We introduce a general model of cascades, including the voter model and the independent cascade model, for which we provide the first algorithm which recovers the graph's edges with high
+probability and ${\cal O}(s\log m)$ measurements where
 $s$ is the maximum degree of the graph and $m$ is the number of nodes.
 Furthermore, we show that our algorithm also recovers the edge weights (the
 parameters of the diffusion process) and is robust in the context of