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Biometrika 1998 85(4):755-770; doi:10.1093/biomet/85.4.755
© 1998 by Biometrika Trust
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Parameter expansion to accelerate EM: The PX-EM algorithm

CHUANHAI LIU, DONALD B. RUBIN and YING NIAN WU

Bell Laboratories, Lucent Technologies Murray Hill, New Jersey 07974, U.S.A.liu{at}research.bell-labs.com
Department of Statistic, Harvard University Cambridge, Massachusetts 02138, U.S.A.rubin{at}hustat.harvard.edu
Department of Statistic, University of Michigan Ann Arbor, Michigan 48109, U.S.A.yingnian{at}umich.edu

The EM algorithm and its extensions are popular tools for modal estimation but are often criticised for their slow convergence. We propose a new method that can often make EM much faster. The intuitive idea is to use a ‘covariance adjustment’ to correct the analysis of the M step, capitalising on extra information captured in the imputed complete data. The way we accomplish this is by parameter expansion; we expand the complete-data model while preserving the observed-data model and use the expanded complete-data model to generate EM. This parameter-expanded EM, PX-EM, algorithm shares the simplicity and stability of ordinary EM, but has a faster rate of convergence since its M step performs a more efficient analysis. The PX-EM algorithm is illustrated for the multivariate t distribution, a random effects model, factor analysis, probit regression and a Poisson imaging model.

Key Words: AECM • Algorithms • Covariance adjustment • ECM • ECME • Factor analysis • Multivariate t distribution • Parameter expansion • Poisson imaging model • Probit regression • Random effects model


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