Empirical hardness of finding optimal Bayesian network structures: algorithm selection and runtime prediction

Various algorithms have been proposed for finding a Bayesian network structure that is guaranteed to maximize a given scoring function. Implementations of state-of-the-art algorithms, solvers , for this Bayesian network structure learning problem rely on adaptive search strategies, such as branch-an...

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Veröffentlicht in:Machine learning Jg. 107; H. 1; S. 247 - 283
Hauptverfasser: Malone, Brandon, Kangas, Kustaa, Järvisalo, Matti, Koivisto, Mikko, Myllymäki, Petri
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.01.2018
Springer Nature B.V
Schlagworte:
Adaptive search techniques
Algorithms
Artificial Intelligence
Bayesian analysis
Computer Science
Control
Integer programming
Linear programming
Machine learning
Mechatronics
Natural Language Processing (NLP)
Predictions
Robotics
Simulation and Modeling
Solvers
Special Issue on Metalearning and Algorithm Selection
State of the art
Statistical models
Structure learning
Empirical hardness
Algorithm selection
Hyperparameter optimization
Bayesian networks
Runtime prediction
Algorithm portfolio
ISSN:0885-6125, 1573-0565
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Zusammenfassung:Various algorithms have been proposed for finding a Bayesian network structure that is guaranteed to maximize a given scoring function. Implementations of state-of-the-art algorithms, solvers , for this Bayesian network structure learning problem rely on adaptive search strategies, such as branch-and-bound and integer linear programming techniques. Thus, the time requirements of the solvers are not well characterized by simple functions of the instance size. Furthermore, no single solver dominates the others in speed. Given a problem instance, it is thus a priori unclear which solver will perform best and how fast it will solve the instance. We show that for a given solver the hardness of a problem instance can be efficiently predicted based on a collection of non-trivial features which go beyond the basic parameters of instance size. Specifically, we train and test statistical models on empirical data, based on the largest evaluation of state-of-the-art exact solvers to date. We demonstrate that we can predict the runtimes to a reasonable degree of accuracy. These predictions enable effective selection of solvers that perform well in terms of runtimes on a particular instance. Thus, this work contributes a highly efficient portfolio solver that makes use of several individual solvers.
Bibliographie:ObjectType-Article-1
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ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-017-5680-2