Collection Statistical Modeling for Shapes and Imaging
Organizer(s)
Date(s)
04/05/2024
Statistical aspects of stochastic algorithms for entropic optimal transportation between probability measures
This talk is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal transportation problems can be rewritten as a non-strongly concave optimisation problem. It allows to implement a Robbins-Monro stochastic algorithm to estimate the Sinkhorn divergence using a sequence of data sampled from one of the two distributions. The main results discussed in this talk are the asymptotic normality of a new recursive estimator of the Sinkhorn divergence between two probability measures in the discrete and semi-discrete settings, and the rate of convergence of the expected excess risk of this estimator in the absence of strong concavity of the objective function. We also discuss the choice of the regularization parameter in the definition of Sinkhorn divergences from the point of view of data smoothing in nonparametric statistics. Numerical experiments on synthetic and real datasets are also provided to illustrate the usefulness of our approach for the estimation of Laguerre Cells.
