Stochastic blockmodel approximation of a graphon: Theory and consistent estimation

Edoardo M Airoldi; Thiago B Costa; Stanley H Chan

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arXiv · 1311.1731

Stochastic blockmodel approximation of a graphon: Theory and consistent estimation

Edoardo M Airoldi·Thiago B Costa·Stanley H Chan

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Abstract

Non-parametric approaches for analyzing network data based on exchangeable graph models (ExGM) have recently gained interest. The key object that defines an ExGM is often referred to as a graphon. This non-parametric perspective on network modeling poses challenging questions on how to make inference on the graphon underlying observed network data. In this paper, we propose a computationally efficient procedure to estimate a graphon from a set of observed networks generated from it. This procedure is based on a stochastic blockmodel approximation (SBA) of the graphon. We show that, by approximating the graphon with a stochastic block model, the graphon can be consistently estimated, that is, the estimation error vanishes as the size of the graph approaches infinity.

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Edoardo M Airoldi, Thiago B Costa, Stanley H Chan. 2013-11-08. Stochastic blockmodel approximation of a graphon: Theory and consistent estimation. https://arxiv.org/abs/1311.1731

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