Supervision : Christophe GONZALES

Co-supervision : WUILLEMIN Pierre-Henri, LEBRUN Régis

Learning non-parametric Copula Bayesian Networks

Modeling multivariate continuous distributions is a task of central interest in statistics and machine learning with many applications in science and engineering. However, high-dimensional distributions are difficult to handle and can lead to intractable computations.
The Copula Bayesian Networks (CBNs) take advantage of both Bayesian networks (BNs) and copula theory to compactly represent such multivariate distributions. Bayesian networks rely on conditional independences in order to reduce the complexity of the problem, while copula functions allow modeling the dependence relation between random variables.
The goal of this thesis is to give a common framework for both domains and to propose new learning algorithms for copula Bayesian networks. To do so, we use the fact that CBNs have the same graphical language as BNs which allow us to adapt their learning methods to this model.
Moreover, using the empirical Bernstein copula both to design conditional independence tests and to estimate copulas from data, we avoid making parametric assumptions, which gives greater generality to our methods.

2018-2022 Publications

• 2022
  • M. Lasserre : “Apprentissages dans les Réseaux Bayésiens à Base de Copules Non-Paramétriques”, thesis, defence 03/11/2022, supervision Gonzales, Christophe, rapporteurs : WUILLEMIN Pierre-Henri, LEBRUN Régis (2022)
• 2021
  • M. Lasserre, R. Lebrun, P.‑H. Wuillemin : “Apprentissage de modèles continus à grandes dimensions en utilisant l’information mutuelle et les réseaux bayésiens de copules”, 10^es Journées Francophones sur les Réseaux Bayésiens et les Modèles Graphiques Probabilistes, Porquerolles, France (2021)
  • M. Lasserre, R. Lebrun, P.‑H. Wuillemin : “Constraint-based learning for non-parametric continuous bayesian networks”, Annals of Mathematics and Artificial Intelligence, vol. 89, pp. 1035-1052, (Springer Verlag) (2021)
  • M. Lasserre, R. Lebrun, P.‑H. Wuillemin : “Learning Continuous High-Dimensional Models using Mutual Information and Copula Bayesian Networks”, Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35 (13), AAAI-21 Technical Tracks 13, Vancouver, Canada, pp. 12139-12146 (2021)
• 2020
  • M. Lasserre, R. Lebrun, P.‑H. Wuillemin : “Constraint-Based Learning for Non-Parametric Continuous Bayesian Networks”, FLAIRS 33 - 33^rd Florida Artificial Intelligence Research Society Conference, Miami, United States, pp. 581-586, (AAAI) (2020)
• 2018
  • A. Goareguer, A. Le Denn, F. Renaude, Ch. Maragna, P.‑H. Wuillemin, M. Lasserre, Ch. Gonzales, M. Clausse : “Projet SunSTONE : réseaux de chaleur solaires intelligents avec stockage intersaisonnier”, Journées Nationales sur l'Energie Solaire - JNES 2018, Lyon, France (2018)