Reference : SISTA: Learning Optimal Transport Costs under Sparsity Constraints
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
SISTA: Learning Optimal Transport Costs under Sparsity Constraints
Dupuy, Arnaud mailto [University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Department of Economics and Management (DEM) >]
Carlier, Guillaume []
Galichon, Alfred []
Sun, Yifei []
In press
Communications on Pure and Applied Mathematics
John Wiley & Sons
Yes (verified by ORBilu)
[en] : inverse optimal transport, coordinate descent, ISTA
[en] 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.
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