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

Titouan Vayer; Etienne Lasalle

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arXiv · 2501.12005

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

Titouan Vayer·Etienne Lasalle

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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.

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Titouan Vayer, Etienne Lasalle. 2025-01-23. A note on the relations between mixture models, maximum-likelihood and entropic optimal transport. https://arxiv.org/abs/2501.12005

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