Statistics for entropic optimal transport with decreasing regularisation

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.