Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
An Algebraic Model for Combinatorial Problems
SIAM Journal on Computing
Computational Statistics & Data Analysis - Nonlinear methods and data mining
Exact Bayesian Structure Discovery in Bayesian Networks
The Journal of Machine Learning Research
Probabilistic partial evaluation: exploiting rule structure in probabilistic inference
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
A Bayesian approach to learning Bayesian networks with local structure
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Learning Bayesian networks with local structure
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
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The conditional distribution of a discrete variable y, given another discrete variable x, is often specified by assigning one multinomial distribution to each state of x. The cost of this rich parametrization is the loss of statistical power in cases where the data actually fits a model with much fewer parameters. In this paper, we consider a model that partitions the state space of x into disjoint sets, and assigns a single Dirichlet-multinomial to each set. We treat the partition as an unknown variable which is to be integrated away when the interest is in a coarser level task, e.g., variable selection or classification. Based on two different computational approaches, we present two exact algorithms for integration over partitions. Respective complexity bounds are derived in terms of detailed problem characteristics, including the size of the data and the size of the state space of x. Experiments on synthetic data demonstrate the applicability of the algorithms.