Scalable Bayesian Network Structure Learning with Splines

Charupriya Sharma, Peter van Beek
Proceedings of The 11th International Conference on Probabilistic Graphical Models, PMLR 186:181-192, 2022.

Abstract

The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions (CPDs) into the score-and-search approach can improve the accuracy of the learned graph. In this paper, we present a novel approach capable of learning the graph of a BN and simultaneously modelling linear and non-linear local probabilistic relationships between variables. We achieve this by a combination of feature selection to reduce the search space for local relationships and extending the score-and-search approach to incorporate modelling the CPDs over variables as Multivariate Adaptive Regression Splines (MARS). MARS are polynomial regression models represented as piecewise spline functions. We show on a set of discrete and continuous benchmark instances that our proposed approach can improve the accuracy of the learned graph while scaling to instances with a large number of variables.

Cite this Paper

BibTeX
@InProceedings{pmlr-v186-sharma22a, title = {Scalable Bayesian Network Structure Learning with Splines}, author = {Sharma, Charupriya and van Beek, Peter}, booktitle = {Proceedings of The 11th International Conference on Probabilistic Graphical Models}, pages = {181--192}, year = {2022}, editor = {Salmerón, Antonio and Rumı́, Rafael}, volume = {186}, series = {Proceedings of Machine Learning Research}, month = {05--07 Oct}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v186/sharma22a/sharma22a.pdf}, url = {https://proceedings.mlr.press/v186/sharma22a.html}, abstract = {The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions (CPDs) into the score-and-search approach can improve the accuracy of the learned graph. In this paper, we present a novel approach capable of learning the graph of a BN and simultaneously modelling linear and non-linear local probabilistic relationships between variables. We achieve this by a combination of feature selection to reduce the search space for local relationships and extending the score-and-search approach to incorporate modelling the CPDs over variables as Multivariate Adaptive Regression Splines (MARS). MARS are polynomial regression models represented as piecewise spline functions. We show on a set of discrete and continuous benchmark instances that our proposed approach can improve the accuracy of the learned graph while scaling to instances with a large number of variables.} }
Endnote
%0 Conference Paper %T Scalable Bayesian Network Structure Learning with Splines %A Charupriya Sharma %A Peter van Beek %B Proceedings of The 11th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2022 %E Antonio Salmerón %E Rafael Rumı́ %F pmlr-v186-sharma22a %I PMLR %P 181--192 %U https://proceedings.mlr.press/v186/sharma22a.html %V 186 %X The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions (CPDs) into the score-and-search approach can improve the accuracy of the learned graph. In this paper, we present a novel approach capable of learning the graph of a BN and simultaneously modelling linear and non-linear local probabilistic relationships between variables. We achieve this by a combination of feature selection to reduce the search space for local relationships and extending the score-and-search approach to incorporate modelling the CPDs over variables as Multivariate Adaptive Regression Splines (MARS). MARS are polynomial regression models represented as piecewise spline functions. We show on a set of discrete and continuous benchmark instances that our proposed approach can improve the accuracy of the learned graph while scaling to instances with a large number of variables.
APA
Sharma, C. & van Beek, P.. (2022). Scalable Bayesian Network Structure Learning with Splines. Proceedings of The 11th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 186:181-192 Available from https://proceedings.mlr.press/v186/sharma22a.html.

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