Structural learning of bayesian networks from ordinal data

Abstract

In observational studies many features are measured on a sample in a given time. When the measurement scale is ordinal, observed variables are categorical ordinal variables. Their increasing presence in databases has in uenced the development of methods for ordinal data analysis (Joe 1971; Clogg and Shihadeh 1994; Agresti 2010). Frequently, researchers are interested in the multivariate analysis and dependencies (Cox and Wermuth 1996). Graphical models (Lauritzen 1996) can be useful for this purpose: they are a family of multivariate statistical models that study dependencies among variables and provide a representation of them by means of graphs. Among these models, Bayesian networks (Cowell et al. 1999) represent the joint distribution of a set of variables using directed acyclic graphs (DAGs). When the structure of phenomenon is unknown (or partially known), building the DAG manually may be di cult, but the network can be learnt directly from data. This phase, called structural learning, can be performed following di erent approaches. However, there are few methods suitable for ordinal data. The main task of this PhD thesis is to perform the structural learning of Bayesian networks in presence of ordinal variables. As original aspect, a new procedure able to take into account information provided by ordinal variables, has been developed. The new algorithm, called OPC, represents a variation of one of the most used and well-known constraint-based algorithms, namely PC (Spirtes et al. 2000). A nonparametric test, appropriate for ordinal variables, has been used in the OPC procedure. Some simulation studies have been conducted in order to evaluate and compare the performance of PC and OPC algorithms. On the basis of results, the main features and limitations of the OPC procedure are discussed.