A Bayesian Approach to Learning Bayesian Networks with Local Structure
This work addresses a specific challenge in probabilistic graphical modeling for researchers in machine learning and statistics, representing an incremental advancement over existing decision-tree-based methods.
The paper tackles the problem of learning Bayesian networks with decision-graph representations for conditional probability distributions using a Bayesian approach, presenting methods for evaluating posterior probabilities and searching high-scoring networks, with experimental evaluation showing improved accuracy over decision-tree methods in some cases.
Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has concentrated on using decision-tree representations for the CPDs. In addition, researchers typically apply non-Bayesian (or asymptotically Bayesian) scoring functions such as MDL to evaluate the goodness-of-fit of networks to the data. In this paper we investigate a Bayesian approach to learning Bayesian networks that contain the more general decision-graph representations of the CPDs. First, we describe how to evaluate the posterior probability that is, the Bayesian score of such a network, given a database of observed cases. Second, we describe various search spaces that can be used, in conjunction with a scoring function and a search procedure, to identify one or more high-scoring networks. Finally, we present an experimental evaluation of the search spaces, using a greedy algorithm and a Bayesian scoring function.