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Title:
Statistics for entropic optimal transport with decreasing regularisation
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Abstract:
In this talk, we will discuss the question of establishing CLTs for empirical entropic optimal transport when choosing the regularisation parameter as a decreasing function of the sample size. Importantly, decreasing the regularisation parameter enables estimating the population unregularized quantities of interest. Furthermore, we will show an application to score function estimation, a central quantity in diffusion models, and will discuss parallels with recent work on the estimation of transport maps based on the linearization of the Monge—Ampère equation.
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