Uma abordagem robusta para a detecção de dependências em modelos de redes bayesianas

Abstract

In many areas of knowledge, there is interest in the joint modeling of random variables. To represent and accommodate the existing dependencies between these variables, a widely used approach considers Bayesian network models. Bayesian networks are defined by two elements: a directed acyclic graph and a probability space related to it. Each node in the graph represents a random variable, while the arcs are the dependencies between them. To detect the graph of a Bayesian Network from a dataset, there are three main classes of algorithms, the score-based, the constraint-based and the hybrid algorithms, something in commom between them is the use of score functions or conditional independence tests that assume multinomial or Gaussian distributions. These kinds of methods were applied on synthetic networks and real data throughout this work, showing the differences they can present and their usability. Additionally, the score-based algorithms were extended to non-Gaussian continuous distributions using a BIC score that assumes an Asymmetric Laplace model. The experiments to compare this score with the BIC variations for Gaussian and discrete networks were promising in synthetic networs and real data. On synthetic networks, outliers were introduced into the data, and in the real-data illustration, a small dataset was used, for which the estimation is more sensitive to extreme values.