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Advances in Bayesian Network Learning using Integer Programming
Mark Bartlett,James Cussens +1 more
TL;DR: In this paper, the problem of learning Bayesian networks (BNs) from complete discrete data is formulated as an integer program, and various steps are taken to allow efficient solving of this IP.
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Abstract: We consider the problem of learning Bayesian networks (BNs) from complete discrete data. This problem of discrete optimisation is formulated as an integer program (IP). We describe the various steps we have taken to allow efficient solving of this IP. These are (i) efficient search for cutting planes, (ii) a fast greedy algorithm to find high-scoring (perhaps not optimal) BNs and (iii) tightening the linear relaxation of the IP. After relating this BN learning problem to set covering and the multidimensional 0-1 knapsack problem, we present our empirical results. These show improvements, sometimes dramatic, over earlier results.
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Citations
Optimization problems for machine learning: A survey
TL;DR: The machine learning literature is surveyed and in an optimization framework several commonly used machine learning approaches are presented for regression, classification, clustering, deep learning, and adversarial learning as well as new emerging applications in machine teaching, empirical modelLearning, and Bayesian network structure learning.
248
A hybrid algorithm for Bayesian network structure learning with application to multi-label learning
TL;DR: The 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.
94
Improved K2 algorithm for Bayesian network structure learning
Shahab Behjati,Hamid Beigy +1 more
TL;DR: This paper proposes a new fast and straightforward algorithm for addressing the problem of learning the structure of Bayesian networks from data, which takes a dataset and outputs a directed acyclic graph, based on an ordering by extracting strongly connected components of the graph built from data.
72
Machine Learning of Bayesian Networks Using Constraint Programming
Peter van Beek,Hella-Franziska Hoffmann +1 more
- 31 Aug 2015
TL;DR: This paper proposes an improved constraint model that includes powerful dominance constraints, symmetry-breaking constraints, cost-based pruning rules, and an acyclicity constraint for effectively pruning the search for a minimum cost solution to the model.
69
•Proceedings Article
Learning Optimal Bounded Treewidth Bayesian Networks via Maximum Satisfiability
Jeremias Berg,Matti Järvisalo,Brandon Malone +2 more
- 02 Apr 2014
TL;DR: This work develops a novel score-based approach to BTW-BNSL, based on casting BTW’s structure as weighted partial Maximum satisability, and demonstrates empirically that the approach scales notably better than a recent exact dynamic programming algorithm for BTw-B NSL.
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Probabilistic graphical models : principles and techniques
Daniel L. Koller,Nir Friedman +1 more
- 31 Jul 2009
TL;DR: The framework of probabilistic graphical models, presented in this book, provides a general approach for causal reasoning and decision making under uncertainty, allowing interpretable models to be constructed and then manipulated by reasoning algorithms.
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Integer programming
George L. Nemhauser,Laurence A. Wolsey +1 more
- 01 Jan 1972
TL;DR: The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization as mentioned in this paper, which is a standard of graduate-level courses since 1972.
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Edmonds polytopes and a hierarchy of combinatorial problems
TL;DR: It is proved that there is no upper bound on the rank of problems arising from the search for largest independent sets in graphs.
680
Constraint Integer Programming
Tobias Achterberg
- 17 Jul 2007
TL;DR: This thesis deals with chip design verification, which is an important topic of electronic design automation, and shows how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole.
•Proceedings Article
A simple approach for finding the globally optimal Bayesian network structure
Tomi Silander,Petri Myllymäki +1 more
- 13 Jul 2006
TL;DR: In this paper, the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC is studied, which is known to be NP-hard and becomes quickly infeasible as the number of variables increases.