Estimating Matching Affinity Matrix Under Low-Rank Constraints
31 Pages Posted: 10 Jan 2017
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Estimating Matching Affinity Matrix under Low-Rank Constraints
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
JEL Classification: C5, D3
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