Bayesian network learning with nominal, ordinal and continuous data

Abstract

Bayesian networks are a type of probabilistic graphic models composed of nodes and directed edges that serve to represent dependencies between the di erent random variables of the problem, as well as the conditional probability distributions associated to said variables. Originally, both the structure of the Network and the probability distributions were thought for discrete data, but due to the wide eld of application of Bayesian Networks, methods have been developed for other types of variables, as well as for problems with variables of various types. In this Master's Degree Dissertation, we seek to understand the operation of the di erent methods that have been developed to deal with the learning of Bayesian Networks with not only discrete variables, but also continuous, ordinal and mixed variables. Although one of the most common methods to treat Bayesian Networks with continuous variables is discretization, and some methods will be brie y explained, an attempt will be made to explain alternative methods to avoid the loss of information and the error with respect to the modelling of reality that it entails. After the completion of the thesis, it is expected to have an understanding of the subject, and to be able to transmit this knowledge to the reader in a clear and concise way. Structure learning methods will be explained, as well as the conditional probability distributions used to represent each kind of variable, together with the parameters to be learned. Also, methods of study of independence such as Mutual Information, and their estimation from a training database will be explained, as well as the Jonckheere-Terpstra Test for ordinal variables