Constraint-Based Learning for Non-Parametric Continuous Bayesian Networks

Overview & Synopsis

Modeling high-dimensional multivariate distributions is a computationally challenging task. Bayesian networks have been successfully used to reduce the complexity and simplify the problem with discrete variables. However, it lacks of a general model for continuous variables. In order to overcome this problem, (Elidan 2010) proposed the model of cop-ula bayesian networks that reparametrizes bayesian networks with conditional copula functions. We propose a new learning algorithm for copula bayesian networks based on a PC algorithm and a conditional independence test proposed by (Bouezmarni, Rombouts, and Taamouti 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 score based method proposed by (El-idan 2010). Not only it proves to be faster, but also it generalizes well on data generated from distributions far from the gaussian model.