Chain Graph Models to Elicit the Structure of a Bayesian Network

Federico M Stefanini

doi:10.1155/2014/749150

Abstract

Bayesian networks are possibly the most successful graphical models to build decision support systems. Building the structure of large networks is still a challenging task, but Bayesian methods are particularly suited to exploit experts' degree of belief in a quantitative way while learning the network structure from data. In this paper details are provided about how to build a prior distribution on the space of network structures by eliciting a chain graph model on structural reference features. Several structural features expected to be often useful during the elicitation are described. The statistical background needed to effectively use this approach is summarized, and some potential pitfalls are illustrated. Finally, a few seminal contributions from the literature are reformulated in terms of structural features.

Highlights

Bayesian networks (BNs) are possibly the most successful graphical models to represent probabilistic and causal relationships [1, 2]
Among the limitations penalizing the use of this prior we found the following: (i) The impossibility of specifying the degree of belief if it depends on the number of different edges δ and on their position and type; the presence/absence/direction of an arrow may have an impact on the belief about other edges
Graphical models may be exploited to elicit beliefs about the structure of an unknown BN from experts

Summary

Introduction

Bayesian networks (BNs) are possibly the most successful graphical models to represent probabilistic and causal relationships [1, 2]. BNs are used in very different fields including medical domains [3], engineering [4], ecology [5], bioinformatics [6], and many others. The core of this class of models is made by a directed acyclic graph (DAG) G, where nodes in the graph are labels of modeled variables (elements of vector X), and oriented edges (arrows) capture probabilistic and/or causal relationships. If substantial prior information is available on a given problem domain, it is possible that an expert defines the structure of G and even the parameters inside the conditional distribution functions at a reasonable extent.

Methods

Results

Discussion

Conclusion