An Nml-based Method for Learning Bayesian Networks

Bayesian networks are among most popular model classes for discrete vector-valued i.i.d data. Currently the most popular model selection criterion for Bayesian networks follows Bayesian paradigm. However, this method has recently been reported to be very sensitive to the choice of prior hyper-parameters [1]. On the other hand, the general model selection criteria, AIC [2] and BIC [3], are derived through asymptotics and their behavior is suboptimal for small sample sizes. This extended abstract is based on an unpublished manuscript [4] in which we introduce a new effective scoring criterion for learning Bayesian network structures, the factorized normalized maximum likelihood (fNML). This score features no tunable parameters thus avoiding the sensitivity problems of Bayesian scores. It also has a probabilistic interpretation which yields a natural way to use the selected model for predicting future data.