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.
Highlights
The performance of machine learning models is highly dependent on the quality of the data that are available to train them: the more information they contain, the better the insights we can obtain from them
We investigate the impact of learning the parameters and the structure of a Bayesian networks (BNs) using hard EM instead of soft EM with a comprehensive simulation study covering incomplete data with a wide array of different characteristics
BN parameter learning from incomplete data is typically performed using the EM algorithm
Summary
The performance of machine learning models is highly dependent on the quality of the data that are available to train them: the more information they contain, the better the insights we can obtain from them. Incomplete data contain, by construction, less useful information to model the phenomenon we are studying because there are fewer complete observations from which to learn the distribution of the variables and their interplay. Modern probabilistic approaches have followed the lead of Rubin [3,4] and modelled missing values along with the stochastic mechanism of missingness. This class of approaches introduces one auxiliary variable for each experimental variable that is not completely observed in order to model the distribution of missingness; Algorithms 2020, 13, 329; doi:10.3390/a13120329 www.mdpi.com/journal/algorithms
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