Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Learning Bayesian networks from data: an information-theory based approach
Artificial Intelligence
The Last-Step Minimax Algorithm
ALT '00 Proceedings of the 11th International Conference on Algorithmic Learning Theory
Optimal structure identification with greedy search
The Journal of Machine Learning Research
Exact Bayesian Structure Discovery in Bayesian Networks
The Journal of Machine Learning Research
The Journal of Machine Learning Research
A linear-time algorithm for computing the multinomial stochastic complexity
Information Processing Letters
Information and Complexity in Statistical Modeling
Information and Complexity in Statistical Modeling
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Theory refinement on Bayesian networks
UAI'91 Proceedings of the Seventh conference on Uncertainty in Artificial Intelligence
Parent assignment is hard for the MDL, AIC, and NML costs
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Fisher information and stochastic complexity
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Feature selection for Bayesian network classifiers using the MDL-FS score
International Journal of Approximate Reasoning
On open questions in the geometric approach to structural learning Bayesian nets
International Journal of Approximate Reasoning
Discriminative Learning of Bayesian Networks via Factorized Conditional Log-Likelihood
The Journal of Machine Learning Research
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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 it provides a way to construct highly predictive Bayesian network models. Our empirical tests show that the proposed method compares favorably with alternative approaches in both model selection and prediction tasks.