Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequality
Machine Learning
2025-11-21 v2 Machine Learning
Optimization and Control
Statistics Theory
Computation
Statistics Theory
Abstract
We present a new framework for analysing the Expectation Maximization (EM) algorithm. Drawing on recent advances in the theory of gradient flows over Euclidean-Wasserstein spaces, we extend techniques from alternating minimization in Euclidean spaces to the EM algorithm, via its representation as coordinate-wise minimization of the free energy. In so doing, we obtain finite sample error bounds and exponential convergence of the EM algorithm under a natural generalisation of the log-Sobolev inequality. We further show that this framework naturally extends to several variants of EM, offering a unified approach for studying such algorithms.
Cite
@article{arxiv.2407.17949,
title = {Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequality},
author = {Rocco Caprio and Adam M Johansen},
journal= {arXiv preprint arXiv:2407.17949},
year = {2025}
}