2021/02/02 by Alexander Korotin, Korotin, Alexander, Lingxiao Li +5 · 1 citation
Computer Science · Environmental Science · Mathematics · #FOS: Computer and information sciences #Geometric Analysis and Curvature Flows #Groundwater flow and contamination studies #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2102.01752
openalex publication_date 2021/02/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Wasserstein barycenters provide a geometric notion of the weighted average of\nprobability measures based on optimal transport. In this paper, we present a\nscalable algorithm to compute Wasserstein-2 barycenters given sample access to\nthe input measures, which are not restricted to being discrete. While past\napproaches rely on entropic or quadratic regularization, we employ input convex\nneural networks and cycle-consistency regularization to avoid introducing bias.\nAs a result, our approach does not resort to minimax optimization. We provide\ntheoretical analysis on error bounds as well as empirical evidence of the\neffectiveness of the proposed approach in low-dimensional qualitative scenarios\nand high-dimensional quantitative experiments.\n