Hybrid Copula Bayesian Networks

Kiran Karra, Lamine Mili
Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:240-251, 2016.

Abstract

This paper introduces the hybrid copula Bayesian network (HCBN) model, a generalization of the copula Bayesian network (CBN) model developed by Elidan (2010) for continuous random variables to multivariate mixed probability distributions of discrete and continuous random variables. To this end, we extend the theorems proved by Nešlehovà (2007) from bivariate to multivariate copulas with discrete and continuous marginal distributions. Using the multivariate copula with discrete and continuous marginal distributions as a theoretical basis, we construct an HCBN that can model all possible permutations of discrete and continuous random variables for parent and child nodes, unlike the popular conditional linear Gaussian network model. Finally, we demonstrate on a numerous synthetic datasets and a real life dataset that our HCBN compares favorably, from a modeling and flexibility viewpoint, to other hybrid models including the conditional linear Gaussian and the mixture of truncated exponentials models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v52-karra16, title = {Hybrid Copula {B}ayesian Networks}, author = {Karra, Kiran and Mili, Lamine}, booktitle = {Proceedings of the Eighth International Conference on Probabilistic Graphical Models}, pages = {240--251}, year = {2016}, editor = {Antonucci, Alessandro and Corani, Giorgio and Campos}, Cassio Polpo}, volume = {52}, series = {Proceedings of Machine Learning Research}, address = {Lugano, Switzerland}, month = {06--09 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v52/karra16.pdf}, url = {https://proceedings.mlr.press/v52/karra16.html}, abstract = {This paper introduces the hybrid copula Bayesian network (HCBN) model, a generalization of the copula Bayesian network (CBN) model developed by Elidan (2010) for continuous random variables to multivariate mixed probability distributions of discrete and continuous random variables. To this end, we extend the theorems proved by Nešlehovà (2007) from bivariate to multivariate copulas with discrete and continuous marginal distributions. Using the multivariate copula with discrete and continuous marginal distributions as a theoretical basis, we construct an HCBN that can model all possible permutations of discrete and continuous random variables for parent and child nodes, unlike the popular conditional linear Gaussian network model. Finally, we demonstrate on a numerous synthetic datasets and a real life dataset that our HCBN compares favorably, from a modeling and flexibility viewpoint, to other hybrid models including the conditional linear Gaussian and the mixture of truncated exponentials models.} }
Endnote
%0 Conference Paper %T Hybrid Copula Bayesian Networks %A Kiran Karra %A Lamine Mili %B Proceedings of the Eighth International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2016 %E Alessandro Antonucci %E Giorgio Corani %E Cassio Polpo Campos} %F pmlr-v52-karra16 %I PMLR %P 240--251 %U https://proceedings.mlr.press/v52/karra16.html %V 52 %X This paper introduces the hybrid copula Bayesian network (HCBN) model, a generalization of the copula Bayesian network (CBN) model developed by Elidan (2010) for continuous random variables to multivariate mixed probability distributions of discrete and continuous random variables. To this end, we extend the theorems proved by Nešlehovà (2007) from bivariate to multivariate copulas with discrete and continuous marginal distributions. Using the multivariate copula with discrete and continuous marginal distributions as a theoretical basis, we construct an HCBN that can model all possible permutations of discrete and continuous random variables for parent and child nodes, unlike the popular conditional linear Gaussian network model. Finally, we demonstrate on a numerous synthetic datasets and a real life dataset that our HCBN compares favorably, from a modeling and flexibility viewpoint, to other hybrid models including the conditional linear Gaussian and the mixture of truncated exponentials models.
RIS
TY - CPAPER TI - Hybrid Copula Bayesian Networks AU - Kiran Karra AU - Lamine Mili BT - Proceedings of the Eighth International Conference on Probabilistic Graphical Models DA - 2016/08/15 ED - Alessandro Antonucci ED - Giorgio Corani ED - Cassio Polpo Campos} ID - pmlr-v52-karra16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 52 SP - 240 EP - 251 L1 - http://proceedings.mlr.press/v52/karra16.pdf UR - https://proceedings.mlr.press/v52/karra16.html AB - This paper introduces the hybrid copula Bayesian network (HCBN) model, a generalization of the copula Bayesian network (CBN) model developed by Elidan (2010) for continuous random variables to multivariate mixed probability distributions of discrete and continuous random variables. To this end, we extend the theorems proved by Nešlehovà (2007) from bivariate to multivariate copulas with discrete and continuous marginal distributions. Using the multivariate copula with discrete and continuous marginal distributions as a theoretical basis, we construct an HCBN that can model all possible permutations of discrete and continuous random variables for parent and child nodes, unlike the popular conditional linear Gaussian network model. Finally, we demonstrate on a numerous synthetic datasets and a real life dataset that our HCBN compares favorably, from a modeling and flexibility viewpoint, to other hybrid models including the conditional linear Gaussian and the mixture of truncated exponentials models. ER -
APA
Karra, K. & Mili, L.. (2016). Hybrid Copula Bayesian Networks. Proceedings of the Eighth International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 52:240-251 Available from https://proceedings.mlr.press/v52/karra16.html.

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