Identifiability of AMP chain graph models
This addresses a theoretical and algorithmic problem for researchers in graphical models and causal inference, offering incremental advances in identifiability conditions and computational methods.
The paper tackles the identifiability of Andersson-Madigan-Perlman (AMP) chain graph models, showing that the DAG on chain components is identifiable under a monotonicity condition on residual covariance determinants, and provides a polynomial-time algorithm for structure recovery when the decomposition is unknown, with experimental comparisons against baselines.
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.