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diff --git a/paper/sections/abstract.tex b/paper/sections/abstract.tex index a07228f..72a9bf4 100644 --- a/paper/sections/abstract.tex +++ b/paper/sections/abstract.tex @@ -1,8 +1,8 @@ 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 |