Hard and Soft EM in Bayesian Network Learning from Incomplete Data

TL;DR

This paper compares hard and soft EM algorithms for learning Bayesian networks from incomplete data, analyzing their impact on model quality and providing guidance for practitioners.

Contribution

It systematically evaluates the effects of imputation versus belief propagation in EM, offering a decision tree for selecting the appropriate method.

Findings

Imputation can be preferable in certain data scenarios.

Belief propagation often yields better models with complex data.

A decision tree guides method choice based on data characteristics.

Abstract

Incomplete data are a common feature in many domains, from clinical trials to industrial applications. Bayesian networks (BNs) are often used in these domains because of their graphical and causal interpretations. BN parameter learning from incomplete data is usually implemented with the Expectation-Maximisation algorithm (EM), which computes the relevant sufficient statistics ("soft EM") using belief propagation. Similarly, the Structural Expectation-Maximisation algorithm (Structural EM) learns the network structure of the BN from those sufficient statistics using algorithms designed for complete data. However, practical implementations of parameter and structure learning often impute missing data ("hard EM") to compute sufficient statistics instead of using belief propagation, for both ease of implementation and computational speed. In this paper, we investigate the question: what is the impact of using imputation instead of belief propagation on the quality of the resulting BNs? From a simulation study using synthetic data and reference BNs, we find that it is possible to recommend one approach over the other in several scenarios based on the characteristics of the data. We then use this information to build a simple decision tree to guide practitioners in choosing the EM algorithm best suited to their problem.