Likelihoods and Parameter Priors for Bayesian Networks
This work addresses the challenge of parameter and structure learning in Bayesian networks for researchers and practitioners, though it appears incremental as it builds on existing assumptions to improve efficiency.
The paper tackles the problem of constructing likelihoods and parameter priors for Bayesian networks by introducing assumptions like likelihood equivalence, enabling efficient learning from limited assessments. It results in methods for computing marginal likelihoods and a framework for characterizing priors in multivariate distributions.
We develop simple methods for constructing likelihoods and parameter priors for learning about the parameters and structure of a Bayesian network. In particular, we introduce several assumptions that permit the construction of likelihoods and parameter priors for a large number of Bayesian-network structures from a small set of assessments. The most notable assumption is that of likelihood equivalence, which says that data can not help to discriminate network structures that encode the same assertions of conditional independence. We describe the constructions that follow from these assumptions, and also present a method for directly computing the marginal likelihood of a random sample with no missing observations. Also, we show how these assumptions lead to a general framework for characterizing parameter priors of multivariate distributions.