On Graph and Hypergraph Inference via Structural Equation Models

Abstract

This article provides an overview of graph and hypergraph learning methods based on nodal observations as well as measurements arising from groups of nodes. We focus on a widely used class of approaches based on structural equation models (SEMs), in which each nodal observation is modeled as a linear combination of other nodal observations and, optionally, products of nodal observations or group-based measurements. These SEMs may also incorporate exogenous variables and noise. In conventional graph learning, the model reduces to a purely linear form by omitting product terms and group measurements, whereas their inclusion enables the recovery of higher-order interaction structures. We review several topology recovery problems, discuss their identifiability conditions, and summarize relevant references.