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Parameter expansion to accelerate EM: The PX-EM algorithm

By Chuanhai Liu, Donald B. Rubin and Ying Nian Wu


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

Topics: Some key words, AECM, Algorithms, Covariance adjustment, ECM, ECME, Factor analysis, Multivariate t distribution, Parameter expansion, Poisson imaging model, Probit regression, Random effects model
Year: 1998
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