Quotient Normalized Maximum Likelihood Criterion for Learning Bayesian Network Structures


Tomi Silander, Janne Leppä-aho, Elias Jääsaari, Teemu Roos ;
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:948-957, 2018.


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.

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