Learning Bayesian networks: a copula approach for mixed-type data

TL;DR

This paper introduces a Bayesian copula-based approach for learning the structure of directed networks from mixed-type data, effectively handling continuous, discrete, ordinal, and binary variables, with applications in social and health sciences.

Contribution

The paper presents a novel Bayesian methodology for structure learning of directed networks that accommodates mixed data types and incorporates prior known dependence structures.

Findings

Outperforms current state-of-the-art methods in simulation studies.

Successfully applied to social survey and mental health data.

Demonstrates flexibility in incorporating prior knowledge.

Abstract

Estimating dependence relationships between variables is a crucial issue in many applied domains, such as medicine, social sciences and psychology. When several variables are entertained, these can be organized into a network which encodes their set of conditional dependence relations. Typically however, the underlying network structure is completely unknown or can be partially drawn only; accordingly it should be learned from the available data, a process known as structure learning. In addition, data arising from social and psychological studies are often of different types, as they can include categorical, discrete and continuous measurements. In this paper we develop a novel Bayesian methodology for structure learning of directed networks which applies to mixed data, i.e. possibly containing continuous, discrete, ordinal and binary variables simultaneously. Whenever available, our method can easily incorporate known dependence structures among variables represented by paths or edge directions that can be postulated in advance based on the specific problem under consideration. We evaluate the proposed method through extensive simulation studies, with appreciable performances in comparison with current state-of-the-art alternative methods. Finally, we apply our methodology to well-being data from a social survey promoted by the United Nations, and mental health data collected from a cohort of medical students.