Quotient Normalized Maximum Likelihood Criterion for Learning Bayesian Network Structures
This work addresses structure learning in Bayesian networks, which is important for probabilistic modeling in fields like machine learning and statistics, but it appears incremental as it builds on existing normalized maximum likelihood criteria.
The authors tackled the problem of Bayesian network structure learning by introducing the quotient normalized maximum likelihood (qNML) criterion, which satisfies score equivalence and is hyperparameter-free, leading to parsimonious models with good predictive accuracy in experiments on simulated and real data.
We introduce an information theoretic criterion for Bayesian network structure learning which we call quotient normalized maximum likelihood (qNML). In contrast to the closely related factorized normalized maximum likelihood criterion, qNML satisfies the property of score equivalence. It is also decomposable and completely free of adjustable hyperparameters. For practical computations, we identify a remarkably accurate approximation proposed earlier by Szpankowski and Weinberger. Experiments on both simulated and real data demonstrate that the new criterion leads to parsimonious models with good predictive accuracy.