Bayesian Discovery of Multiple Bayesian Networks via Transfer Learning

Bayesian network structure learning algorithms with limited data are being used in domains such as systems biology and neuroscience to gain insight into the underlying processes that produce observed data. Learning reliable networks from limited data is difficult, therefore transfer learning can improve the robustness of learned networks by leveraging data from related tasks. Existing transfer learning algorithms for Bayesian network structure learning give a single maximum a posteriori estimate of network models. Yet, many other models may be equally likely, and so a more informative result is provided by Bayesian structure discovery. Bayesian structure discovery algorithms estimate posterior probabilities of structural features, such as edges. We present transfer learning for Bayesian structure discovery which allows us to explore the shared and unique structural features among related tasks. Efficient computation requires that our transfer learning objective factors into local calculations, which we prove is given by a broad class of transfer biases. Theoretically, we show the efficiency of our approach. Empirically, we show that compared to single task learning, transfer learning is better able to positively identify true edges. We apply the method to whole-brain neuroimaging data.Comment: 10 page

Learning Credal Sum-Product Networks

Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational bottleneck being inference that is intractable. Tractable learning is a powerful new paradigm that attempts to learn distributions that support efficient probabilistic querying. By leveraging local structure, representations such as sum-product networks (SPNs) can capture high tree-width models with many hidden layers, essentially a deep architecture, while still admitting a range of probabilistic queries to be computable in time polynomial in the network size. While the progress is impressive, numerous data sources are incomplete, and in the presence of missing data, structure learning methods nonetheless revert to single distributions without characterizing the loss in confidence. In recent work, credal sum-product networks, an imprecise extension of sum-product networks, were proposed to capture this robustness angle. In this work, we are interested in how such representations can be learnt and thus study how the computational machinery underlying tractable learning and inference can be generalized for imprecise probabilities.Comment: Accepted to AKBC 202

Learning Bayesian networks with local structure, mixed variables, and exact algorithms

Modern exact algorithms for structure learning in Bayesian networks first compute an exact local score of every candidate parent set, and then find a network structure by combinatorial optimization so as to maximize the global score. This approach assumes that each local score can be computed fast, which can be problematic when the scarcity of the data calls for structured local models or when there are both continuous and discrete variables, for these cases have lacked efficient-to-compute local scores. To address this challenge, we introduce a local score that is based on a class of classification and regression trees. We show that under modest restrictions on the possible branchings in the tree structure, it is feasible to find a structure that maximizes a Bayes score in a range of moderate-size problem instances. In particular, this enables global optimization of the Bayesian network structure, including the local structure. In addition, we introduce a related model class that extends ordinary conditional probability tables to continuous variables by employing an adaptive discretization approach. The two model classes are compared empirically by learning Bayesian networks from benchmark real-world and synthetic data sets. We discuss the relative strengths of the model classes in terms of their structure learning capability, predictive performance, and running time. (C) 2019 The Authors. Published by Elsevier Inc.Peer reviewe