TY  - RPRT
        AU  - Dupuy, Arnaud
AU  - Galichon, Alfred
AU  - Sun, Yifei
        TI  - Estimating Matching Affinity Matrix under Low-Rank Constraints
        PY  - 2016/Dec/
        PB  - Institute of Labor Economics (IZA)
        CY  - Bonn
        T2  - IZA Discussion Paper
        IS  - 10449
        UR  - https://www.iza.org/publications/dp10449
        AB  - 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.
        KW  - inverse optimal transport
KW  - rank-constrained estimation
KW  - bipartite matching
KW  - marriage market
        ER  -