Reference : Estimating Matching Affinity Matrix under Low-Rank Constraints
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
Estimating Matching Affinity Matrix under Low-Rank Constraints
Dupuy, Arnaud mailto [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]
Information and Inference: a Journal of the IMA
[en] inverse optimal transport ; rank-constrained estimation ; bipartite matching
[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.
FnR ; FNR8337045 > Arnaud Dupuy > CHILDCARE > Optimal policies in the market for childcare: theory and evidence from Luxembourg > 01/05/2015 > 30/04/2018 > 2014

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