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The community detection problem involves observing the edges of a graph and making inferences about vertex labels (community labels) that are statistically related to the edges. Applications include recommendation systems, social media analysis, and fraud detection. This problem is often modeled with a stochastic block model, a generalization of the Erdos-Renyi graph in which the edge probabilities depend on the identity of the vertices (nodes) at which they terminate. In the last decade, much progress has been made in inference using the stochastic block model, in particular conditions for asymptotic recovery in certain regimes are now known. Our work is motivated by the usual presence of non-graphical data, which we call "side information," along with (and related with) graphical data.  We discuss the influence of non-graphical side information on community detection via analyzing the inference phase transition threshold. This threshold essentially expresses which problems (graphs) are fundamentally solvable, which ones are not, and when and how does side information change that distinction. For the two-community problem, the effect of partially revealed labels and noisy label side information is discussed. A more general side information with arbitrary alphabet consisting of k features is studied. Implications of these results will be discussed. 

Green Building GR Building

Natural Sciences & Mathematics
Viswanath Ramakrishna
Email
972-883-6873

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