2018/10/23 by Marcel Klatt, Klatt, Marcel, Carla Tameling +3 · 2 citations
Mathematics · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1810.09880
We derive limit distributions for certain empirical regularized optimal\ntransport distances between probability distributions supported on a finite\nmetric space and show consistency of the (naive) bootstrap. In particular, we\nprove that the empirical regularized transport plan itself asymptotically\nfollows a Gaussian law. The theory includes the Boltzmann-Shannon entropy\nregularization and hence a limit law for the widely applied Sinkhorn\ndivergence. Our approach is based on an application of the implicit function\ntheorem to necessary and sufficient optimality conditions for the regularized\ntransport problem. The asymptotic results are investigated in Monte Carlo\nsimulations. We further discuss computational and statistical applications,≠.g. confidence bands for colocalization analysis of protein interaction\nnetworks based on regularized optimal transport.\n