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

TL;DR

This paper introduces a spectral-based pseudo-metric for graph data and uses it to estimate probability distributions of large graphs, demonstrating effective approximation of complex distributions.

Contribution

It proposes a novel spectral pseudo-metric for graph sets and applies it to infer graph distribution parameters, enhancing graph probability density estimation.

Findings

Spectral pseudo-metric effectively captures graph similarities.

Sample moments under this metric accurately approximate complex distributions.

Method demonstrates strong empirical approximation capabilities.

Abstract

For graph-valued data sampled iid from a distribution $\mu$, 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 $\ell_2$ 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 $\hat{\mu}$ and interpret this distribution as an approximation of $\mu$. We verify experimentally that complex distributions $\mu$ can be approximated well taking this approach.