Regularised optimal self-transport is approximate Gaussian mixture maximum likelihood

2023/10/23 by Mordant, Gilles
#62H30 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2310.14851

Abstract

We investigate the link between regularised self-transport problems and maximum likelihood estimation in Gaussian mixture models (GMM). This link suggests that self-transport followed by a clustering technique leads to principled estimators at a reasonable computational cost. Also, robustness, sparsity and stability properties of the optimal transport plan arguably make the regularised self-transport a statistical tool of choice for the GMM.

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