Learning networks determined by the ratio of prior and data
This work provides incremental theoretical insights for researchers in Bayesian network learning, clarifying the role of prior specification in model selection.
The paper tackled the problem of learning Bayesian network structures by analyzing how the equivalent sample size (ESS) of a Dirichlet prior influences arc selection, showing that the ratio of ESS to sample size determines the penalty for adding arcs, with arc count increasing as ESS rises and decreasing as ESS falls.
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.