Abstract
Modeling high-dimensional multivariate distributions is a computationally challenging task. In the discrete case, Bayesian networks have been successfully used to reduce the complexity and to simplify the problem. However, they lack of a general model for continuous variables. In order to overcome this problem, Elidan (2010) proposed the model of copula Bayesian networks that parametrizes Bayesian networks using copula functions. We propose a new learning algorithm for this model based on a PC algorithm and a conditional independence test proposed by Bouezmarni et al. (2009). This test being non-parametric, no model assumptions are made allowing it to be as general as possible. This algorithm is compared on generated data with the parametric method proposed by Elidan (2010) and proves to have better results.
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The source code for CBIC and CPC methods is available on the GitHub repository openturns/otagrum.
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This work was partially supported by Airbus Research through the AtRandom project (CRT/VPE/XRD).
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Lasserre, M., Lebrun, R. & Wuillemin, PH. Constraint-based learning for non-parametric continuous bayesian networks. Ann Math Artif Intell 89, 1035–1052 (2021). https://doi.org/10.1007/s10472-021-09754-2
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DOI: https://doi.org/10.1007/s10472-021-09754-2