Linearly preconditioned nonlinear conjugate gradient acceleration of the PX-EM algorithm

• Published in: Computational statistics & data analysis Vol. 155; p. 107056
• Main Authors: Zhou, Lin, Tang, Yayong
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2021
• Subjects: acceleration; AEM algorithm; algorithms; data analysis; estimation; Factor analysis; Generalized gradient; hybrids; Linearly PNCG algorithm; PX-EM algorithm; Random effects; statistical models; Random effects; Factor analysis; PX-EM algorithm; Linearly PNCG algorithm; AEM algorithm; Generalized gradient
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2020.107056

The EM algorithm is a widely applicable algorithm for modal estimation but often criticized for its slow convergence. A new hybrid accelerator named APX-EM is proposed for speeding up the convergence of EM algorithm, which is based on both Linearly Preconditioned Nonlinear Conjugate Gradient (PNCG) and PX-EM algorithm. The intuitive idea is that, each step of the PX-EM algorithm can be viewed approximately as a generalized gradient just like the EM algorithm, then the linearly PNCG method can be used to accelerate the EM algorithm. Essentially, this method is an adjustment of the AEM algorithm, and it usually achieves a faster convergence rate than the AEM algorithm by sacrificing a little simplicity. The convergence of the APX-EM algorithm, includes a global convergence result for this method under suitable conditions, is discussed. This method is illustrated for factor analysis and a random-effects model.