Title: Asymptotic inference for Multimarginal Optimal Transport cost
Speaker: Natalia Kravtsova (The Ohio State Univeristy)
Speaker's URL: https://kravtsova2.github.io/
Abstract: Multimarginal Optimal Transport cost is a generalization of the Wasserstein distance to more than two probability measures. When this cost is estimated from empirical measures in place of their true counterparts, the resulting object is a random variable whose asymptotic distribution is derived in this work. The asymptotic distributions are provided for a certain class of measures relevant in scientific applications and are proved using techniques from sensitivity analysis of random linear programs. The results are used to construct statistical inference procedures based on the asymptotic behavior of the Multimarginal Optimal Transport cost. The consistency of the bootstrap schemes used to sample from asymptotic distributions is shown, and performance of recently proposed algorithms for computing the desired estimates is evaluated. The utility of the proposed approach is demonstrated on various datasets, including the real data on lung cancer in the US population in 2004 - 2020.
URL associated with Seminar: https://tgda.osu.edu/
