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SISTA : Learning Optimal Transport Costs under Sparsity Constraints

Author

Listed:
  • Guillaume Carlier

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres, MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales - CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique - Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique)

  • Arnaud Dupuy

    (uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg)

  • Alfred Galichon

    (CIMS - Courant Institute of Mathematical Sciences [New York] - NYU - New York University [New York] - NYU - NYU System, ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Yifei Sun

    (CIMS - Courant Institute of Mathematical Sciences [New York] - NYU - New York University [New York] - NYU - NYU System)

Abstract

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.

Suggested Citation

  • Guillaume Carlier & Arnaud Dupuy & Alfred Galichon & Yifei Sun, 2022. "SISTA : Learning Optimal Transport Costs under Sparsity Constraints," Post-Print hal-03893060, HAL.
    • Handle: RePEc:hal:journl:hal-03893060
    DOI: 10.1002/cpa.22047
    as

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