%0 Journal Article %T Estimating Matching Affinity Matrices under Low-Rank Constraints %+ University of Luxemburg %+ NYU System (NYU) %+ Courant Institute of Mathematical Sciences [New York] (CIMS) %+ Département d'économie (Sciences Po) (ECON) %A Dupuy, Arnaud %A Galichon, Alfred %A Sun, Yifei %Z Luxembourg National Research Fund (FNR) (grant C14/SC/8337045 to A.D.); National Science Foundation (NSF) (grant DMS-1716489 to A.G.). %< avec comité de lecture %@ 2049-8764 %J Information and Inference %I Oxford University Press (OUP) %V 8 %N 4 %P 677-689 %8 2019-12 %D 2019 %R 10.1093/imaiai/iaz015 %Z Humanities and Social Sciences/Economics and FinanceJournal articles %X 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 that effectively enforces a rank constraint on the affinity matrix. The low-rank matrix estimated in this way reveals the main factors that are relevant for matching. %G English %L hal-03948102 %U https://sciencespo.hal.science/hal-03948102 %~ SHS %~ SCIENCESPO %~ CNRS %~ AO-ECONOMIE %~ USPC %~ ECON-SCPO %~ SCPO-REPEC