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The Graph Pencil Method: Mapping Subgraph Densities to Stochastic Block Models

Lee Gunderson · Gecia Bravo-Hermsdorff · Peter Orbanz

Great Hall & Hall B1+B2 (level 1) #1401
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[ Paper [ Poster [ OpenReview
Thu 14 Dec 3 p.m. PST — 5 p.m. PST


In this work, we describe a method that determines an exact map from a finite set of subgraph densities to the parameters of a stochastic block model (SBM) matching these densities. Given a number K of blocks, the subgraph densities of a finite number of stars and bistars uniquely determines a single element of the class of all degree-separated stochastic block models with K blocks. Our method makes it possible to translate estimates of these subgraph densities into model parameters, and hence to use subgraph densities directly for inference. The computational overhead is negligible; computing the translation map is polynomial in K, but independent of the graph size once the subgraph densities are given.

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