A Legacy of EM Algorithms. (12th October 2022)

• Record Type: Journal Article
• Authors: Lange, Kenneth; Zhou, Hua
• Is Part Of: International statistical review. Volume 90(2022)Supplement 1
• Page Start: S52
• Page End: S66
• Publication Date: 2022-10-12
• Subjects: EM algorithm -- MM algorithm -- variance component model -- longitudinal data analysis; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12526
• Languages: English
• ISSNs: 0306-7734

Abstract

Summary: Nan Laird has an enormous and growing impact on computational statistics. Her paper with Dempster and Rubin on the expectation‐maximisation (EM) algorithm is the second most cited paper in statistics. Her papers and book on longitudinal modelling are nearly as impressive. In this brief survey, we revisit the derivation of some of her most useful algorithms from the perspective of the minorisation‐maximisation (MM) principle. The MM principle generalises the EM principle and frees it from the shackles of missing data and conditional expectations. Instead, the focus shifts to the construction of surrogate functions via standard mathematical inequalities. The MM principle can deliver a classical EM algorithm with less fuss or an entirely new algorithm with a faster rate of convergence. In any case, the MM principle enriches our understanding of the EM principle and suggests new algorithms of considerable potential in high‐dimensional settings where standard algorithms such as Newton's method and Fisher scoring falter.