Acceleration of the EM, MM, and Other Monotone Algorithms for Modern Applications

Various convergence acceleration techniques developed in computational mathematics can and have been applied to speed up the convergence of EM and MM algorithms. This monograph will present and discuss these convergence acceleration schemes, with applications and demonstrations using R and Julia code. The monograph will likely be useful to PhD-level graduate students and researchers in statistics, data science, applied mathematics, engineering, and physics working on computational algorithms for big data and high-dimensional problems.

Basics of Convergence Acceleration (e.g., Aitken’s extrapolation, Extension to Vector Sequences, Polynomial Extrapolation, etc.). EM Algorithm and its Convergence, Examples, Slow Convergence. MM Algorithm, Examples, Slow Convergence. Other Monotone Algorithms in Statistics. Acceleration of EM, MM, etc. Nesterov Acceleration Applied to Gradient Descent Algorithm. Acceleration Techniques for Bayesian Computing (Hamiltonian Monte-Carlo). Convergence Acceleration for Modern Applications (High-Dimensional Problems, Nonlinear Models, Big Data). Description of R packages and Julia software.

Dr. Varadhan is an Associate Professor of Oncology in the Division of Biostatistics and Bioinformatics at the Sidney Kimmel Comprehensive Cancer Center (SKCCC). He is also a core faculty in the Center on Aging and Health and the Center for Drug Safety and Effectiveness. Dr. Varadhan is a well-known expert in several areas of biostatistics. He is an expert in the area of patient-centered outcomes research (PCOR), where he focuses on developing statistical methods that inform evidence-based individualized medicine. He has a particular interest in Bayesian methods for exploring heterogeneity of treatment effect (HTE). He has developed numerous algorithms and software for solving high-dimensional optimization problems arising in statistical modeling. Hua Zhou teaches and does research in biostatistics at the University of California, Los Angeles (UCLA). She received her Ph.D. in 2008 from the Department of Statistics at Stanford University.