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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 35 / No. 13: AAAI-21 Technical Tracks 13

Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks

February 1, 2023

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Authors

Marvin Lasserre

Laboratoire d'Informatique de Paris 6


Régis Lebrun

Airbus Central Research & Technology


Pierre-Henri Wuillemin

Laboratoire d'Informatique de Paris 6


DOI:

10.1609/aaai.v35i13.17441


Abstract:

We propose a new framework to learn non-parametric graphical models from continuous observational data. Our method is based on concepts from information theory in order to discover independences and causality between variables: the conditional and multivariate mutual information (such as cite{verny2017learning} for discrete models). To estimate these quantities, we propose non-parametric estimators relying on the Bernstein copula and that are constructed by exploiting the relation between the mutual information and the copula entropy cite{ma2011mutual, belalia2017testing}. To our knowledge, this relation is only documented for the bivariate case and, for the need of our algorithms, is here extended to the conditional and multivariate mutual information. This framework leads to a new algorithm to learn continuous non-parametric Bayesian network. Moreover, we use this estimator to speed up the BIC algorithm proposed in cite{elidan2010copula} by taking advantage of the decomposition of the likelihood function in a sum of mutual information cite{koller2009probabilistic}. Finally, our method is compared in terms of performances and complexity with other state of the art techniques to learn Copula Bayesian Networks and shows superior results. In particular, it needs less data to recover the true structure and generalizes better on data that are not sampled from Gaussian distributions.

Topics: AAAI

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HOW TO CITE:

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks Proceedings of the AAAI Conference on Artificial Intelligence (2021) 12139-12146.

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks AAAI 2021, 12139-12146.

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin (2021). Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks. Proceedings of the AAAI Conference on Artificial Intelligence, 12139-12146.

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin. Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks. Proceedings of the AAAI Conference on Artificial Intelligence 2021 p.12139-12146.

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin. 2021. Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks. "Proceedings of the AAAI Conference on Artificial Intelligence". 12139-12146.

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin. (2021) "Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks", Proceedings of the AAAI Conference on Artificial Intelligence, p.12139-12146

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin, "Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks", AAAI, p.12139-12146, 2021.

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin. "Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks". Proceedings of the AAAI Conference on Artificial Intelligence, 2021, p.12139-12146.

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin. "Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks". Proceedings of the AAAI Conference on Artificial Intelligence, (2021): 12139-12146.

Marvin Lasserre||Régis Lebrun||Pierre-Henri Wuillemin. Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks. AAAI[Internet]. 2021[cited 2023]; 12139-12146.


ISSN: 2374-3468


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