COMPUTATIONAL STRATEGIES FOR STATISTICAL INFERENCE BASED ON EMPIRICAL OPTIMAL TRANSPORT

In this paper we discuss some recent limit laws for empirical optimal transport distances from a simulation perspective. On discrete spaces, this requires to solve another optimal transport problem in each simulation step, which reveals simulations of such limit laws computational demanding. We discuss several strategies, e.g., resampling, to overcome this burden. In particular, we examine empirically an upper bound for such limiting distributions on discrete spaces based on a spanning tree approximation which can be computed explicitly.