Introduction to structure learning for gaussian and pair copula bayesian networks

Abstract

Due to technological breakthrough in recent decades and the rapid increase in the availability of multidimensional data, data science has become one of the most important areas of research. Within this field, modeling dependence of random variables is gaining great interest. To cope with this task, the use of graphical models is often advocated. In this dissertation, we study Bayesian Networks (BNs), a particular type of graphical models. Concretely, structure learning algorithms for two types of continuous BNs: Gaussian Bayesian Networks (GBNs) and Pair Copula Bayesian Network (PCBNs) are investigated.

We present an overview of these two types of BNs, illustrating its properties and differences. An outline of the different existing structure learning algorithms is provided, showing their efficiency for the Gaussian case and limitations for the copula based. The problems of structure learning for PCBNs are then addressed. We investigate the performance of Gaussian structure learning algorithms for PCBNs. Based on a simulation study, we show that these procedures are not completely efficient, but prove beneficial. Second, a new approximation of the score based on logLikelihood of PCBNs is explored. We propose to solve the computational inefficiency of the exact logLikelihood by estimating the necessary copulas from data such that the copula terms in the PCBNs decomposition can be computed without need of integration. A simulation study suggests that this logLikelihood approximation yields better results than the approximation used
by Pircalabelu et al. (2017). Finally, an algorithm to learn the structure of PCBNs is proposed, based on the 2 previous procedures.