Maximum-likelihood estimation for discrete mixture models is equivalent to minimizing an entropic optimal transport objective, and EM is block-coordinate descent on that objective.
Sinkhorn distances: Lightspeed computation of optimal transport
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A note on the relations between mixture models, maximum-likelihood and entropic optimal transport
Maximum-likelihood estimation for discrete mixture models is equivalent to minimizing an entropic optimal transport objective, and EM is block-coordinate descent on that objective.