Search

Score functions for learning the structure of Bayesian networks in the literature assume that data are a homogeneous set of observations; whereas it is often the case that they comprise different related, but not homogeneous, data sets collected in different ways. In this paper we propose a new Bayesian Dirichlet score, which we call Bayesian Hierarchical Dirichlet (BHD). The proposed score is based on a hierarchical model that pools information across data sets to learn a single encompassing network structure, while taking into account the differences in their probabilistic structures. We derive a closed-form expression for BHD using a variational approximation of the marginal likelihood, we study the associated computational cost and we evaluate its performance using simulated data. We find that, when data comprise multiple related data sets, BHD outperforms the Bayesian Dirichlet equivalent uniform (BDeu) score in terms of reconstruction accuracy as measured by the Structural Hamming distance, and that it is as accurate as BDeu when data are homogeneous. This improvement is particularly clear when either the number of variables in the network or the number of observations is large. Moreover, the estimated networks are sparser and therefore more interpretable than those obtained with BDeu thanks to a lower number of false positive arcs. [ABSTRACT FROM AUTHOR]

PRISM is a probabilistic logic programming formalism which allows defining a probability distribution over possible worlds. This paper investigates learning a class of generative PRISM programs known as failure-free. The aim is to learn recursive PRISM programs which can be used to model stochastic processes. These programs generalise dynamic Bayesian networks by defining a halting distribution over the generative process. Dynamic Bayesian networks model infinite stochastic processes. Sampling from infinite process can only be done by specifying the length of sequences that the process generates. In this case, only observations of a fixed length of sequences can be obtained. On the other hand, the recursive PRISM programs considered in this paper are self-terminating upon some halting conditions. Thus, they generate observations of different lengths of sequences. The direction taken by this paper is to combine ideas from inductive logic programming and learning Bayesian networks to learn PRISM programs. It builds upon the inductive logic programming approach of learning from entailment. [ABSTRACT FROM AUTHOR]

The space of Bayesian network structures is prohibitively large and hence numerous techniques have been developed to prune this search space, but without eliminating the optimal structure. Such techniques are critical for structure learning to scale to larger datasets with more variables. Prior works exploited properties of the MDL score to prune away large regions of the search space that can be safely ignored by optimal structure learning algorithms. In this paper, we propose new techniques for pruning regions of the search space that can be safely ignored by algorithms that enumerate the k -best Bayesian network structures. Empirically, these techniques allow a state-of-the-art structure enumeration algorithm to scale to datasets with significantly more variables. [ABSTRACT FROM AUTHOR]

Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods [24,29] tackle the problem by using k -trees to learn the optimal Bayesian network with tree-width up to k . Finding the best k -tree, however, is computationally intractable. In this paper, we propose a sampling method to efficiently find representative k -trees by introducing an informative score function to characterize the quality of a k -tree. To further improve the quality of the k -trees, we propose a probabilistic hill climbing approach that locally refines the sampled k -trees. The proposed algorithm can efficiently learn a quality Bayesian network with tree-width at most k . Experimental results demonstrate that our approach is more computationally efficient than the exact methods with comparable accuracy, and outperforms most existing approximate methods. [ABSTRACT FROM AUTHOR]