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

• URL: http://arxiv.org/abs/2501.12005v2
• Date: Thu, 23 Jan 2025 09:47:30 GMT
• Title: A note on the relations between mixture models, maximum-likelihood and entropic optimal transport
• Authors: Titouan Vayer, Etienne Lasalle,
• Abstract summary: We show that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization.
• Score: 6.246185995463311
• License:
• 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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