Identifiability of Linear AMP Chain Graph Models

Authors

  • Yuhao Wang National University of Singapore
  • Arnab Bhattacharyya National University of Singapore

DOI:

https://doi.org/10.1609/aaai.v36i9.21247

Keywords:

Reasoning Under Uncertainty (RU), Machine Learning (ML), Knowledge Representation And Reasoning (KRR)

Abstract

We study identifiability of linear 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 equal (or more generally, 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.

Downloads

Published

2022-06-28

How to Cite

Wang, Y., & Bhattacharyya, A. (2022). Identifiability of Linear AMP Chain Graph Models. Proceedings of the AAAI Conference on Artificial Intelligence, 36(9), 10080-10089. https://doi.org/10.1609/aaai.v36i9.21247

Issue

Section

AAAI Technical Track on Reasoning under Uncertainty