Estimating Matching Affinity Matrices under Low-Rank Constraints - Sciences Po Access content directly
Journal Articles Information and Inference Year : 2019

Estimating Matching Affinity Matrices 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 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.
No file

Dates and versions

hal-03948102 , version 1 (19-01-2023)

Identifiers

Cite

Arnaud Dupuy, Alfred Galichon, Yifei Sun. Estimating Matching Affinity Matrices under Low-Rank Constraints. Information and Inference, 2019, 8 (4), pp.677-689. ⟨10.1093/imaiai/iaz015⟩. ⟨hal-03948102⟩
14 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More