On Supervised Selection of Bayesian Networks

TL;DR

This paper evaluates various model selection criteria for Bayesian networks in supervised tasks, finding that the Dawids prequential approach outperforms the traditional marginal likelihood score in predictive accuracy.

Contribution

It provides an empirical comparison of supervised model selection methods, highlighting the limitations of marginal likelihood and the effectiveness of Dawids prequential criterion.

Findings

Marginal likelihood performs poorly in supervised Bayesian network selection.

Dawids prequential approach yields the best predictive performance.

Empirical results are based on numerous publicly available classification datasets.

Abstract

Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In contrast to this, in supervised model selection it is a priori known that the chosen model will be used in the future for prediction tasks involving more ``focused' predictive distributions. Although focused predictive distributions can be produced from the joint probability distribution by marginalization, in practice the best model in the unsupervised sense does not necessarily perform well in supervised domains. In particular, the standard marginal likelihood score is a criterion for the unsupervised task, and, although frequently used for supervised model selection also, does not perform well in such tasks. In this paper we study the performance of the marginal likelihood score empirically in supervised Bayesian network selection tasks by using a large number of publicly available classification data sets, and compare the results to those obtained by alternative model selection criteria, including empirical crossvalidation methods, an approximation of a supervised marginal likelihood measure, and a supervised version of Dawids prequential(predictive sequential) principle.The results demonstrate that the marginal likelihood score does NOT perform well FOR supervised model selection, WHILE the best results are obtained BY using Dawids prequential r napproach.