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Register a new userA hybrid algorithm for Bayesian network structure learning with application to multi-label learning
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Maxime Gasse
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We present a novel hybrid algorithm for Bayesian network structure learning, called H2PC. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. The algorithm is based on divide-and-conquer constraint-based subroutines to learn the local structure around a target variable. We conduct two series of experimental comparisons of H2PC against Max-Min Hill-Climbing (MMHC), which is currently the most powerful state-of-the-art algorithm for Bayesian network structure learning. First, we use eight well-known Bayesian network benchmarks with various data sizes to assess the quality of the learned structure returned by the algorithms. Our extensive experiments show that H2PC outperforms MMHC in terms of goodness of fit to new data and quality of the network structure with respect to the true dependence structure of the data. Second, we investigate H2PCs ability to solve the multi-label learning problem. We provide theoretical results to characterize and identify graphically the so-called minimal label powersets that appear as irreducible factors in the joint distribution under the faithfulness condition. The multi-label learning problem is then decomposed into a series of multi-class classification problems, where each multi-class variable encodes a label powerset. H2PC is shown to compare favorably to MMHC in terms of global classification accuracy over ten multi-label data sets covering different application domains. Overall, our experiments support the conclusions that local structural learning with H2PC in the form of local neighborhood induction is a theoretically well-motivated and empirically effective learning framework that is well suited to multi-label learning. The source code (in R) of H2PC as well as all data sets used for the empirical tests are publicly available.
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We present a novel hybrid algorithm for Bayesian network structure learning, called Hybrid HPC (H2PC). It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. It is based on a subroutine called HPC, that combines ideas from incremental and divide-and-conquer constraint-based methods to learn the parents and children of a target variable. We conduct an experimental comparison of H2PC against Max-Min Hill-Climbing (MMHC), which is currently the most powerful state-of-the-art algorithm for Bayesian network structure learning, on several benchmarks with various data sizes. Our extensive experiments show that H2PC outperforms MMHC both in terms of goodness of fit to new data and in terms of the quality of the network structure itself, which is closer to the true dependence structure of the data. The source code (in R) of H2PC as well as all data sets used for the empirical tests are publicly available.
We develop a novel hybrid method for Bayesian network structure learning called partitioned hybrid greedy search (pHGS), composed of three distinct yet compatible new algorithms: Partitioned PC (pPC) accelerates skeleton learning via a divide-and-conquer strategy, $p$-value adjacency thresholding (PATH) effectively accomplishes parameter tuning with a single execution, and hybrid greedy initialization (HGI) maximally utilizes constraint-based information to obtain a high-scoring and well-performing initial graph for greedy search. We establish structure learning consistency of our algorithms in the large-sample limit, and empirically validate our methods individually and collectively through extensive numerical comparisons. The combined merits of pPC and PATH achieve significant computational reductions compared to the PC algorithm without sacrificing the accuracy of estimated structures, and our generally applicable HGI strategy reliably improves the estimation structural accuracy of popular hybrid algorithms with negligible additional computational expense. Our empirical results demonstrate the superior empirical performance of pHGS against many state-of-the-art structure learning algorithms.
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Active learning is usually applied to acquire labels of informative data points in supervised learning, to maximize accuracy in a sample-efficient way. However, maximizing the accuracy is not the end goal when the results are used for decision-making, for example in personalized medicine or economics. We argue that when acquiring samples sequentially, separating learning and decision-making is sub-optimal, and we introduce a novel active learning strategy which takes the down-the-line decision problem into account. Specifically, we introduce a novel active learning criterion which maximizes the expected information gain on the posterior distribution of the optimal decision. We compare our decision-making-aware active learning strategy to existing alternatives on both simulated and real data, and show improved performance in decision-making accuracy.
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