  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.
