Estimating Matching Affinity Matrix under Low-Rank Constraints

Arnaud Dupuy (), Alfred Galichon and Yifei Sun
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Yifei Sun: New York University

No 10449, IZA Discussion Papers from Institute of Labor Economics (IZA)

Abstract: 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 species 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 lowrank matrix estimated in this way reveals the main factors which are relevant for matching.

Keywords: inverse optimal transport; rank-constrained estimation; bipartite matching; marriage market (search for similar items in EconPapers)
JEL-codes: C5 D3 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2016-12
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Published - published in: Information and Inference: A Journal of the Institute of Mathematics and its Applications, 2019, 8(4), 677–689..

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