  Bayesian networks are a powerful framework for studying the dependency
structure of variables in a complex system. The problem of learning Bayesian
networks is tightly associated with the given data type. Ordinal data, such as
stages of cancer, rating scale survey questions, and letter grades for exams,
are ubiquitous in applied research. However, existing solutions are mainly for
continuous and nominal data. In this work, we propose an iterative
score-and-search method - called the Ordinal Structural EM (OSEM) algorithm -
for learning Bayesian networks from ordinal data. Unlike traditional approaches
designed for nominal data, we explicitly respect the ordering amongst the
categories. More precisely, we assume that the ordinal variables originate from
marginally discretizing a set of Gaussian variables, whose structural
dependence in the latent space follows a directed acyclic graph. Then, we adopt
the Structural EM algorithm and derive closed-form scoring functions for
efficient graph searching. Through simulation studies, we illustrate the
superior performance of the OSEM algorithm compared to the alternatives and
analyze various factors that may influence the learning accuracy. Finally, we
demonstrate the practicality of our method with a real-world application on
psychological survey data from 408 patients with co-morbid symptoms of
obsessive-compulsive disorder and depression.
