References of "Sun, Yifei"
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See detailSISTA: Learning Optimal Transport Costs under Sparsity Constraints
Dupuy, Arnaud UL; Carlier, Guillaume; Galichon, Alfred et al

in Communications on Pure and Applied Mathematics (in press)

In this paper, we describe a novel iterative procedure called SISTA to learn the underlying cost in optimal transport problems. SISTA is a hybrid between two classical methods, coordinate descent (“S” ... [more ▼]

In this paper, we describe a novel iterative procedure called SISTA to learn the underlying cost in optimal transport problems. SISTA is a hybrid between two classical methods, coordinate descent (“S”-inkhorn) and proximal gradient descent (“ISTA”). It alternates between a phase of exact minimization over the transport potentials and a phase of proximal gradient descent over the parameters of the transport cost. We prove that this method converges linearly, and we illustrate on simulated examples that it is significantly faster than both coordinate descent and ISTA. We apply it to estimating a model of migration, which predicts the flow of migrants using country-specific characteristics and pairwise measures of dissimilarity between countries. This application demonstrates the effectiveness of machine learning in quantitative social sciences. [less ▲]

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See detailEstimating Matching Affinity Matrix under Low-Rank Constraints
Dupuy, Arnaud UL; Galichon, Alfred; Sun, Yifei

in Information and Inference: a Journal of the IMA (2019), 8(4), 677689

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 ... [more ▼]

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. [less ▲]

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