Efficient convergence through adaptive learning in sequential Monte Carlo Expectation Maximization

TL;DR

This paper introduces IOEM, an adaptive online EM algorithm that automatically adjusts learning rates, achieving efficiency comparable or superior to traditional methods in latent variable models.

Contribution

The paper proposes IOEM, an adaptive learning rate algorithm for online EM that removes the need for manual tuning, improving efficiency in complex models.

Findings

IOEM matches the efficiency of optimal BEM and OEM algorithms.

IOEM outperforms BEM/OEM with fixed learning rates in high-parameter models.

The method is validated across multiple models with publicly available implementation.

Abstract

Expectation maximization (EM) is a technique for estimating maximum-likelihood parameters of a latent variable model given observed data by alternating between taking expectations of sufficient statistics, and maximizing the expected log likelihood. For situations where sufficient statistics are intractable, stochastic approximation EM (SAEM) is often used, which uses Monte Carlo techniques to approximate the expected log likelihood. Two common implementations of SAEM, Batch EM (BEM) and online EM (OEM), are parameterized by a "learning rate", and their efficiency depend strongly on this parameter. We propose an extension to the OEM algorithm, termed Introspective Online Expectation Maximization (IOEM), which removes the need for specifying this parameter by adapting the learning rate according to trends in the parameter updates. We show that our algorithm matches the efficiency of the optimal BEM and OEM algorithms in multiple models, and that the efficiency of IOEM can exceed that of BEM/OEM methods with optimal learning rates when the model has many parameters. A Python implementation is available at https://github.com/luntergroup/IOEM.git.