论文标题
SISTA：在稀疏限制下学习最佳运输成本
SISTA: learning optimal transport costs under sparsity constraints
论文作者
论文摘要
在本文中，我们描述了一种名为Sista的新型迭代程序，以学习最佳运输问题中的基本成本。 SISTA是两种经典方法之间的杂种，即坐标下降（“ S” -Inkhorn）和近端梯度下降（“ ISTA”）。它在运输电位上的精确最小化相位与运输成本参数的近端梯度下降相位。我们证明了该方法线性收敛，并在模拟示例上说明了它的速度明显比坐标下降和ISTA更快。我们将其应用于估计移民模型，该模型使用国家特定的特征和成对的国家之间的差异来预测移民的流动。该应用显示了机器学习在定量社会科学中的有效性。
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.
