Damped Anderson acceleration with restarts and monotonicity control for accelerating EM and EM-like algorithms

TL;DR

This paper introduces a new, scalable acceleration method for EM algorithms that significantly speeds up convergence using Anderson acceleration with restarts and damping, applicable across various models.

Contribution

The paper presents a novel, model-agnostic acceleration scheme for EM algorithms that enhances convergence speed and robustness through restarts and damping, outperforming existing methods.

Findings

Substantially faster convergence than existing schemes

Effective in high-dimensional and complex problems

Robust and easy to implement as an off-the-shelf method

Abstract

The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed slow convergence which often hinders the application of EM algorithms in high-dimensional problems or in other complex settings.To address the need for more rapidly convergent EM algorithms, we describe a new class of acceleration schemes that build on the Anderson acceleration technique for speeding fixed-point iterations. Our approach is effective at greatly accelerating the convergence of EM algorithms and is automatically scalable to high dimensional settings. Through the introduction of periodic algorithm restarts and a damping factor, our acceleration scheme provides faster and more robust convergence when compared to un-modified Anderson acceleration while also improving global convergence. Crucially, our method works as an "off-the-shelf" method in that it may be directly used to accelerate any EM algorithm without relying on the use of any model-specific features or insights. Through a series of simulation studies involving five representative problems, we show that our algorithm is substantially faster than the existing state-of-art acceleration schemes.