A note on the relations between mixture models, maximum-likelihood and entropic optimal transport

2025/01/21 by Titouan Vayer, Etienne Lasalle, Vayer, Titouan +1 · 1 voice · 1 citation
#stat.ML #cs.LG

paper · pdf · doi:10.48550/arxiv.2501.12005

Abstract

This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek to present this already known result in a concise and hopefully simple manner. We give an illustration with Gaussian mixture models by showing that the standard EM algorithm is a specific block-coordinate descent on an optimal transport loss.

Cited by

• Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transport

Discussions

• A note on the relations between mixture models, maximum-likelihood and entropic optimal transport As they note, this is an interesting summary written for clarity rather than a new result. But, I've [bsky, 40 points, 1 comments]

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