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Article

Hard and Soft EM in Bayesian Network Learning from Incomplete Data

1
Department of Informatics, Systems and Communication, Università degli Studi di Milano-Bicocca, 20126 Milano, Italy
2
Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA), 6962 Viganello, Switzerland
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Algorithms 2020, 13(12), 329; https://doi.org/10.3390/a13120329
Received: 18 November 2020 / Revised: 7 December 2020 / Accepted: 7 December 2020 / Published: 9 December 2020
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. View Full-Text
Keywords: Bayesian networks; incomplete data; Expectation-Maximisation; parameter learning; structure learning Bayesian networks; incomplete data; Expectation-Maximisation; parameter learning; structure learning
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MDPI and ACS Style

Ruggieri, A.; Stranieri, F.; Stella, F.; Scutari, M. Hard and Soft EM in Bayesian Network Learning from Incomplete Data. Algorithms 2020, 13, 329. https://doi.org/10.3390/a13120329

AMA Style

Ruggieri A, Stranieri F, Stella F, Scutari M. Hard and Soft EM in Bayesian Network Learning from Incomplete Data. Algorithms. 2020; 13(12):329. https://doi.org/10.3390/a13120329

Chicago/Turabian Style

Ruggieri, Andrea, Francesco Stranieri, Fabio Stella, and Marco Scutari. 2020. "Hard and Soft EM in Bayesian Network Learning from Incomplete Data" Algorithms 13, no. 12: 329. https://doi.org/10.3390/a13120329

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