Parameter expansion to accelerate EM: The PX-EM algorithm

• 成果类型: Article
• 署名作者: Liu, CH; Rubin, DB; Wu, YN
• 署名单位: AT&T; Alcatel-Lucent; Lucent Technologies; Nokia Corporation; Nokia Bell Labs; Harvard University; University of Michigan System; University of Michigan
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/85.4.755
• 发表日期: 1998
• 页码: 755770
• 关键词: multivariate t-distribution; maximum-likelihood; EFFECTS MODELS; ml-estimation; CONVERGENCE; ecm; tomography; emission

摘要

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.