SQUAREM: An R Package for Off-the-Shelf Acceleration of EM, MM and Other EM-like Monotone Algorithms

TL;DR

SQUAREM is an R package that accelerates slow, monotone convergence algorithms like EM and MM, significantly reducing computation time across various applications without requiring user parameter tuning.

Contribution

The paper introduces SQUAREM, a simple, general, off-the-shelf R package that accelerates EM-like algorithms with linear convergence, especially effective in high-dimensional and time-consuming scenarios.

Findings

SQUAREM significantly speeds up EM/MM algorithms in diverse applications.

It is easy to implement without parameter tuning.

Performance gains are especially large in high-dimensional problems.

Abstract

We discuss R package SQUAREM for accelerating iterative algorithms which exhibit slow, monotone convergence. These include the well-known expectation-maximization algorithm, majorize-minimize (MM), and other EM-like algorithms such as expectation conditional maximization, and generalized EM algorithms. We demonstrate the simplicity, generality, and power of SQUAREM through a wide array of applications of EM/MM problems, including binary Poisson mixture, factor analysis, interval censoring, genetics admixture, and logistic regression maximum likelihood estimation (an MM problem). We show that SQUAREM is easy to apply, and can accelerate any fixed-point, smooth, contraction mapping with linear convergence rate. Squared iterative scheme (Squarem) algorithm provides significant speed-up of EM-like algorithms. The margin of the advantage for Squarem is especially huge for high-dimensional problems or when EM step is relatively time-consuming to evaluate. Squarem can be used off-the-shelf since there is no need for the user to tweak any control parameters to optimize performance. Given its remarkable ease of use, Squarem may be considered as a default accelerator for slowly converging EM-like algorithms. All the comparisons of CPU computing time in the paper are made on a quad-core 2.3 GHz Intel Core i7 Mac computer. R Package SQUAREM can be downloaded at https://cran.r-project.org/web/packages/SQUAREM/index.html.