Microscopic Advances with Large-Scale Learning: Stochastic Optimization for Cryo-EM

TL;DR

This paper applies stochastic optimization techniques to Cryo-EM density estimation, significantly improving speed and convergence from random initializations in 3D structure determination of biological molecules.

Contribution

It introduces stochastic optimization methods to Cryo-EM structure estimation, demonstrating faster convergence and better performance than existing approaches.

Findings

Some methods recover structures in less than one epoch

Complex quasi-Newton methods converge more slowly than gradient-based methods

All stochastic methods reach similar optima

Abstract

Determining the 3D structures of biological molecules is a key problem for both biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising technique for structure estimation which relies heavily on computational methods to reconstruct 3D structures from 2D images. This paper introduces the challenging Cryo-EM density estimation problem as a novel application for stochastic optimization techniques. Structure discovery is formulated as MAP estimation in a probabilistic latent-variable model, resulting in an optimization problem to which an array of seven stochastic optimization methods are applied. The methods are tested on both real and synthetic data, with some methods recovering reasonable structures in less than one epoch from a random initialization. Complex quasi-Newton methods are found to converge more slowly than simple gradient-based methods, but all stochastic methods are found to converge to similar optima. This method represents a major improvement over existing methods as it is significantly faster and is able to converge from a random initialization.