Monotone Algorithms (original) (raw)

Monotone algorithms, particularly the minorize-maximize (MM) algorithm, play a crucial role in maximum likelihood estimation (MLE). The expectation maximization (EM) algorithm is a specific case of MM but can exhibit slow convergence. This paper introduces squared iterative methods (SQUAREM) as an efficient way to enhance the convergence rate of MM algorithms, especially in high-dimensional problems. SQUAREM demonstrates simplicity and minimal storage requirements, outperforming traditional numerical accelerators, with applications in multi-dimensional scaling, genetic admixture, PET imaging, and movie ratings.