From 3680c9e694f41b00b2bdf51d141fe7d0466b8751 Mon Sep 17 00:00:00 2001 From: jeanpouget-abadie Date: Fri, 6 Feb 2015 12:26:32 -0500 Subject: abstract --- paper/sections/abstract.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) (limited to 'paper/sections') 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 -- cgit v1.2.3-70-g09d2