Identifiability of AMP chain graph models

TL;DR

This paper investigates the conditions under which AMP chain graph models are identifiable, providing new criteria and algorithms for structure recovery, including when the chain component decomposition is unknown.

Contribution

It introduces a monotonic determinant condition for identifiability and a polynomial-time algorithm for recovering the full structure without known decomposition.

Findings

The DAG on chain components is identifiable under the monotone determinant condition.

A polynomial-time algorithm for structure recovery when the decomposition is unknown.

Experimental results show the algorithm outperforms existing methods.

Abstract

We study identifiability of Andersson-Madigan-Perlman (AMP) chain graph models, which are a common generalization of linear structural equation models and Gaussian graphical models. AMP models are described by DAGs on chain components which themselves are undirected graphs. For a known chain component decomposition, we show that the DAG on the chain components is identifiable if the determinants of the residual covariance matrices of the chain components are monotone non-decreasing in topological order. This condition extends the equal variance identifiability criterion for Bayes nets, and it can be generalized from determinants to any super-additive function on positive semidefinite matrices. When the component decomposition is unknown, we describe conditions that allow recovery of the full structure using a polynomial time algorithm based on submodular function minimization. We also conduct experiments comparing our algorithm's performance against existing baselines.