[en] 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.
Disciplines :
Mathematics
Author, co-author :
DUPUY, Arnaud ; University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Center for Research in Economic Analysis (CREA)
Galichon, Alfred; New York University > Economics
Sun, Yifei; New York University > Mathematics
External co-authors :
yes
Language :
English
Title :
Estimating Matching Affinity Matrix under Low-Rank Constraints
Publication date :
2019
Journal title :
Information and Inference: a Journal of the IMA
Volume :
8
Issue :
4
Pages :
677–689
Peer reviewed :
Peer reviewed
Focus Area :
Computational Sciences
FnR Project :
FNR8337045 - Optimal Policies In The Market For Childcare: Theory And Evidence From Luxembourg, 2014 (01/05/2015-30/04/2018) - Arnaud Dupuy