2016/12/30 by Arnaud Dupuy, Alfred Galichon, Dupuy, Arnaud +3 · 1 citation
Mathematics · #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.1612.09585
openalex publication_date 2016/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal joint distribution. In contrast, we study the inverse problem of estimating matching affinity based on the observation of the joint distribution, using an entropic regularization of the problem. To accommodate high dimensionality of the data, we propose a novel method that incorporates a nuclear norm regularization which effectively enforces a rank constraint on the affinity matrix. The low-rank matrix estimated in this way reveals the main factors which are relevant for matching.