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. © 2022 Wiley Periodicals LLC.

中文翻译：

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SISTA：学习稀疏约束下的最优运输成本

在本文中，我们描述了一种称为 SISTA 的新颖迭代过程，用于了解最优运输问题的潜在成本。SISTA 是坐标下降法（“S”-inkhorn）和近端梯度下降法（“ISTA”）这两种经典方法的混合体。它在传输潜力的精确最小化阶段和传输成本参数的近端梯度下降阶段之间交替。我们证明了该方法线性收敛，并且通过模拟示例说明它比坐标下降和 ISTA 都要快得多。我们将其应用于估计移民模型，该模型使用国家特定特征和国家之间差异的成对度量来预测移民流动。该应用程序展示了机器学习在定量社会科学中的有效性。