Learning networks determined by the ratio of prior and data

TL;DR

This paper analyzes how the ratio of prior strength to data size influences the structure learning of Bayesian networks, revealing that the ESS-to-sample ratio controls the complexity of the learned network.

Contribution

It provides an asymptotic analysis showing the ESS-to-sample ratio determines the penalty for adding arcs in Bayesian network learning.

Findings

Number of arcs increases with higher ESS

Number of arcs decreases with lower ESS

Marginal likelihood score unifies various scoring metrics

Abstract

Recent reports have described that the equivalent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymptotic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size determine the penalty of adding arcs in learning Bayesian networks. The number of arcs increases monotonically as the ESS increases; the number of arcs monotonically decreases as the ESS decreases. Furthermore, the marginal likelihood score provides a unified expression of various score metrics by changing prior knowledge.