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.
@InProceedings{pmlr-v52-karra16,
title = {Hybrid Copula {B}ayesian Networks},
author = {Kiran Karra and Lamine Mili},
booktitle = {Proceedings of the Eighth International Conference on Probabilistic Graphical Models},
pages = {240--251},
year = {2016},
editor = {Alessandro Antonucci and Giorgio Corani and Cassio Polpo Campos}},
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 = {http://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.}
}
%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
%J Proceedings of Machine Learning Research
%P 240--251
%U http://proceedings.mlr.press
%V 52
%W PMLR
%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.
TY - CPAPER
TI - Hybrid Copula Bayesian Networks
AU - Kiran Karra
AU - Lamine Mili
BT - Proceedings of the Eighth International Conference on Probabilistic Graphical Models
PY - 2016/08/15
DA - 2016/08/15
ED - Alessandro Antonucci
ED - Giorgio Corani
ED - Cassio Polpo Campos}
ID - pmlr-v52-karra16
PB - PMLR
SP - 240
DP - PMLR
EP - 251
L1 - http://proceedings.mlr.press/v52/karra16.pdf
UR - http://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 -
Karra, K. & Mili, L.. (2016). Hybrid Copula Bayesian Networks. Proceedings of the Eighth International Conference on Probabilistic Graphical Models, in PMLR 52:240-251
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