Integer Linear Programming for the Bayesian network structure learning problem

Bartlett, Mark; Cussens, James

doi:10.1016/j.artint.2015.03.003

Cited by 121 publications

(103 citation statements)

References 16 publications

(23 reference statements)

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“…Bounds greater than 2 can already become prohibitive. For instance, a bound of k = 2 is adopted in [8] when dealing with its largest data set (diabetes), which contains 413 variables. One way of circumventing the problem is to apply pruning rules which allow us to discard/ignore elements of L i in such a way that an optimal parent set is never discarded/ignored.…”

Section: Structure Learning Of Bayesian Networkmentioning

confidence: 99%

Entropy-based pruning for learning Bayesian networks using BIC

Campos¹,

Scanagatta²,

Corani³

et al. 2018

Artificial Intelligence

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For decomposable score-based structure learning of Bayesian networks, existing approaches first compute a collection of candidate parent sets for each variable and then optimize over this collection by choosing one parent set for each variable without creating directed cycles while maximizing the total score. We target the task of constructing the collection of candidate parent sets when the score of choice is the Bayesian Information Criterion (BIC). We provide new non-trivial results that can be used to prune the search space of candidate parent sets of each node. We analyze how these new results relate to previous ideas in the literature both theoretically and empirically. We show in experiments with UCI data sets that gains can be significant. Since the new pruning rules are easy to implement and have low computational costs, they can be promptly integrated into all state-ofthe-art methods for structure learning of Bayesian networks.

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Section: Structure Learning Of Bayesian Networkmentioning

confidence: 99%

Entropy-based pruning for learning Bayesian networks using BIC

Campos¹,

Scanagatta²,

Corani³

et al. 2018

Artificial Intelligence

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show abstract

“…Unfortunately, it has been proved that learning an optimal BN is NP-hard [20]. One practical approach to dealing with the intractable complexity is to learn a constrained or totally pre-fixed network structure.…”

Section: Naive Bayesmentioning

confidence: 99%

“…Given seven algorithms and 40 datasets, CD can be calculated with Equation (20) and is equal to 1.4245. Following the graphical presentation proposed by Demšar [31], we show the comparison of these algorithms against each other with the Nemenyi test in Figure 5.…”

Section: As Shown Inmentioning

confidence: 99%

Label-Driven Learning Framework: Towards More Accurate Bayesian Network Classifiers through Discrimination of High-Confidence Labels

Sun

Wang

Sun

2017

Entropy

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Bayesian network classifiers (BNCs) have demonstrated competitive classification accuracy in a variety of real-world applications. However, it is error-prone for BNCs to discriminate among high-confidence labels. To address this issue, we propose the label-driven learning framework, which incorporates instance-based learning and ensemble learning. For each testing instance, high-confidence labels are first selected by a generalist classifier, e.g., the tree-augmented naive Bayes (TAN) classifier. Then, by focusing on these labels, conditional mutual information is redefined to more precisely measure mutual dependence between attributes, thus leading to a refined generalist with a more reasonable network structure. To enable finer discrimination, an expert classifier is tailored for each high-confidence label. Finally, the predictions of the refined generalist and the experts are aggregated. We extend TAN to LTAN (Label-driven TAN) by applying the proposed framework. Extensive experimental results demonstrate that LTAN delivers superior classification accuracy to not only several state-of-the-art single-structure BNCs but also some established ensemble BNCs at the expense of reasonable computation overhead.

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“…The search is implemented as a branch-and-cut approach, the essentials of which are outlined next. The IP formulation [Bartlett and Cussens, 2017] with which we work is shown in Figure 1. The binary IP variables used, x i←J , correspond to node i having the set of nodes J as parents in the network.…”

Section: Bn Structure Learningmentioning

confidence: 99%

“…Learning an optimal BN structure is a computationally challenging problem: even the restriction of the BNSL problem where only BDe scores [Heckerman et al, 1995] are allowed is known to be NP-hard [Chickering, 1996]. Due to NP-hardness, much work on BNSL has focused on developing approximate, local search style algorithms [Tsamardinos et al, 2006] that in general cannot guarantee that optimal structures in terms of the objective function are found.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Network Structure Learning with Integer Programming: Polytopes, Facets and Complexity (Extended Abstract)

Cussens

Järvisalo

Korhonen

et al. 2017

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

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Developing accurate algorithms for learning structures of probabilistic graphical models is an important problem within modern AI research. Here we focus on score-based structure learning for Bayesian networks as arguably the most central class of graphical models. A successful generic approach to optimal Bayesian network structure learning (BNSL), based on integer programming (IP), is implemented in the GOBNILP system. Despite the recent algorithmic advances, current understanding of foundational aspects underlying the IP based approach to BNSL is still somewhat lacking. In this paper, we provide theoretical contributions towards understanding fundamental aspects of cutting planes and the related separation problem in this context, ranging from NP-hardness results to analysis of polytopes and the related facets in connection to BNSL.

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Integer Linear Programming for the Bayesian network structure learning problem

Cited by 121 publications

References 16 publications

Entropy-based pruning for learning Bayesian networks using BIC

Entropy-based pruning for learning Bayesian networks using BIC

Label-Driven Learning Framework: Towards More Accurate Bayesian Network Classifiers through Discrimination of High-Confidence Labels

Bayesian Network Structure Learning with Integer Programming: Polytopes, Facets and Complexity (Extended Abstract)

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