Journal of Machine Learning Research 12 (2011) 2181-2210 Submitted 4/11; Published 7/11
Discriminative Learning of Bayesian Networks via Factorized Conditional Log-Likelihood
Alexandra M. Carvalho [email protected] Department of Electrical Engineering Instituto Superior Tecnico,´ Technical University of Lisbon INESC-ID, R. Alves Redol 9 1000-029 Lisboa, Portugal
Teemu Roos [email protected] Department of Computer Science Helsinki Institute for Information Technology P.O. Box 68 FI-00014 University of Helsinki, Finland
Arlindo L. Oliveira [email protected] Department of Computer Science and Engineering Instituto Superior Tecnico,´ Technical University of Lisbon INESC-ID, R. Alves Redol 9 1000-029 Lisboa, Portugal
Petri Myllymaki¨ [email protected] Department of Computer Science Helsinki Institute for Information Technology P.O. Box 68 FI-00014 University of Helsinki, Finland
Editor: Russell Greiner
Abstract
We propose an efficient and parameter-free scoring criterion, the factorized conditional log-likelihood (fCLL),ˆ for learning Bayesian network classifiers. The proposed score is an ap- proximation of the conditional log-likelihood criterion. The approximation is devised in order to guarantee decomposability over the network structure, as well as efficient estimation of the optimal parameters, achieving the same time and space complexity as the traditional log-likelihood scoring criterion. The resulting criterion has an information-theoretic interpretation based on interaction information, which exhibits its discriminative nature. To evaluate the performance of the proposed criterion, we present an empirical comparison with state-of-the-art classifiers. Results on a large suite of benchmark data sets from the UCI repository show that fCLL-trainedˆ classifiers achieve at least as good accuracy as the best compared classifiers, using significantly less computational resources.
Keywords: Bayesian networks, discriminative learning, conditional log-likelihood, scoring crite- rion, classification, approximation