2017/11/07 by Vivien Seguy, Seguy, Vivien, Bharath Bhushan Damodaran +9 · 38 citations
Engineering · Mathematics · #Markov Chains and Monte Carlo Methods #Sparse and Compressive Sensing Techniques #Traffic Prediction and Management Techniques #stat.ML
paper · pdf · doi:10.48550/arxiv.1711.02283
15 pages, 4 figures. To appear in the Proceedings of the International Conference on Learning Representations (ICLR) 2018
arxiv created 2018/02/26 · arxiv updated 2018/02/27
This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two distributions. To that end, we propose a stochastic dual approach of regularized OT, and show empirically that it scales better than a recent related approach when the amount of samples is very large. Second, we estimate a Monge map as a deep neural network learned by approximating the barycentric projection of the previously-obtained OT plan. This parameterization allows generalization of the mapping outside the support of the input measure. We prove two theoretical stability results of regularized OT which show that our estimations converge to the OT plan and Monge map between the underlying continuous measures. We showcase our proposed approach on two applications: domain adaptation and generative modeling.