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diff --git a/paper/sections/abstract.tex b/paper/sections/abstract.tex index ad5b893..a07228f 100644 --- a/paper/sections/abstract.tex +++ b/paper/sections/abstract.tex @@ -1,10 +1,11 @@ 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 an algorithm which recovers the graph edges with high probability -provided that the number of measurements is $\Omega(s\log m)$ where $s$ is the -maximum degree of the graph and $m$ is the number of nodes. +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 +$s$ 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 approximate sparsity. Finally we prove an almost matching lower bound of -$\Omega(s\log\frac{m}{s})$. +$\Omega(s\log\frac{m}{s})$ and validate our approach empirically on synthetic +graphs. |