Probability density estimation for sets of large graphs with respect to spectral information using stochastic block models

2022/07/05 by Daniel Ferguson, Ferguson, Daniel, François G. Meyer +1
Mathematics · Computer Science · #Statistical Methods and Inference #Bayesian Modeling and Causal Inference #Bayesian Methods and Mixture Models

paper · pdf · doi:10.48550/arxiv.2207.02168

Abstract

For graph-valued data sampled iid from a distribution μ, the sample moments are computed with respect to a choice of metric. In this work, we equip the set of graphs with the pseudo-metric defined by the ℓ₂ norm between the eigenvalues of the respective adjacency matrices. We use this pseudo metric and the respective sample moments of a graph valued data set to infer the parameters of a distribution μ and interpret this distribution as an approximation of μ. We verify experimentally that complex distributions μ can be approximated well taking this approach.

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