Statistics for entropic optimal transport with decreasing regularisation

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.

The Kantorovich Initiative