Network Topology Inference with Graphon Spectral Penalties

TL;DR

This paper introduces a convex optimization approach for inferring graph structures from data, incorporating prior knowledge from graphon models to improve accuracy, demonstrated through experiments on synthetic and real data.

Contribution

It proposes a novel spectral regularizer based on graphon models for graph Laplacian inference, extending existing methods with prior distribution information.

Findings

Incorporating graphon priors improves inference accuracy.

The method performs well even with imperfect prior knowledge.

Numerical experiments validate the approach on synthetic and real data.

Abstract

We consider the problem of inferring the unobserved edges of a graph from data supported on its nodes. In line with existing approaches, we propose a convex program for recovering a graph Laplacian that is approximately diagonalizable by a set of eigenvectors obtained from the second-order moment of the observed data. Unlike existing work, we incorporate prior knowledge about the distribution from where the underlying graph was drawn. In particular, we consider the case where the graph was drawn from a graphon model, and we supplement our convex optimization problem with a provably-valid regularizer on the spectrum of the graph to be recovered. We present the cases where the graphon model is assumed to be known and the more practical setting where the relevant features of the model are inferred from auxiliary network observations. Numerical experiments on synthetic and real-world data illustrate the advantage of leveraging the proposed graphon prior, even when the prior is imperfect.