Learning locally minimax optimal Bayesian networks

We consider the problem of learning Bayesian network models in a non-informative setting, where the only available information is a set of observational data, and no background knowledge is available. The problem can be divided into two different subtasks: learning the structure of the network (a set of independence relations), and learning the parameters of the model (that fix the probability distribution from the set of all distributions consistent with the chosen structure). There are not many theoretical frameworks that consistently handle both these problems together, the Bayesian framework being an exception. In this paper we propose an alternative, information-theoretic framework which sidesteps some of the technical problems facing the Bayesian approach. The framework is based on the minimax-optimal Normalized Maximum Likelihood (NML) distribution, which is motivated by the Minimum Description Length (MDL) principle. The resulting model selection criterion is consistent, and...

• Type: Journal
• Year: 2010
• Where: IJAR
• Authors: Tomi Silander, Teemu Roos, Petri Myllymäki
• Keywords: Bayesian Network Models, IJAR 2010, Model Selection, Predictive Bayesian Network