Inferring Graphs from Cascades: A Sparse Recovery Framework
This addresses the problem of inferring unknown graphs from diffusion data for applications like social network analysis, but it is incremental as it builds on sparse recovery methods.
The paper tackles the Network Inference problem by recovering graph edges from cascades using a sparse recovery framework, achieving high-probability recovery with O(s log m) measurements where s is the maximum degree and m is the number of nodes, and also recovers edge weights with robustness to approximate sparsity.
In the Network Inference problem, one seeks to recover the edges of an unknown 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 $O(s\log m)$ 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 approximate sparsity. Finally we prove an almost matching lower bound of $Ω(s\log\frac{m}{s})$ and validate our approach empirically on synthetic graphs.