Learning Essential Graph Markov Models From Data

In a model selection procedure where many models are to be compared, computational efficiency is critical. For acyclic digraph (ADG) Markov models (aka DAG models or Bayesian networks), each ADG Markov equivalence class can be represented by a unique chain graph, called an essential graph (EG). This parsimonious representation might be used to facilitate selection among ADG models. Because EGs combine features of decomposable graphs and ADGs, a scoring metric can be developed for EGs with categorical (multinomial) data. This metric may permit the characterization of local computations directly for EGs, which in turn would yield a learning procedure that does not require transformation to representative ADGs at each step for scoring purposes, nor is the scoring metric constrained by Markov equivalence.