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SISTA: Learning Optimal Transport Costs under Sparsity Constraints

Author

Listed:
  • Carlier, Guillaume

    (Université Paris-Dauphine)

  • Dupuy, Arnaud

    (University of Luxembourg)

  • Galichon, Alfred

    (New York University)

  • Sun, Yifei

    (New York University)

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.

Suggested Citation

  • Carlier, Guillaume & Dupuy, Arnaud & Galichon, Alfred & Sun, Yifei, 2021. "SISTA: Learning Optimal Transport Costs under Sparsity Constraints," IZA Discussion Papers 14397, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp14397
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    References listed on IDEAS

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    1. Arnaud Dupuy & Alfred Galichon, 2014. "Personality Traits and the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 122(6), pages 1271-1319.
    2. Mayer, Thierry & Zignago, Soledad, 2006. "Notes on CEPII’s distances measures," MPRA Paper 26469, University Library of Munich, Germany.
    3. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    4. Caglar Ozden & Christopher R. Parsons & Maurice Schiff & Terrie L. Walmsley, 2011. "Where on Earth is Everybody? The Evolution of Global Bilateral Migration 1960-2000," The World Bank Economic Review, World Bank, vol. 25(1), pages 12-56, May.
    5. Michèle Belot & Sjef Ederveen, 2012. "Cultural barriers in migration between OECD countries," Journal of Population Economics, Springer;European Society for Population Economics, vol. 25(3), pages 1077-1105, July.
    6. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    7. Michel Beine & Simone Bertoli & Jesús Fernández-Huertas Moraga, 2016. "A Practitioners’ Guide to Gravity Models of International Migration," The World Economy, Wiley Blackwell, vol. 39(4), pages 496-512, April.
    8. Michel Beine & Christopher Parsons, 2015. "Climatic Factors as Determinants of International Migration," Scandinavian Journal of Economics, Wiley Blackwell, vol. 117(2), pages 723-767, April.
    9. Ron Boschma & Simona Iammarino & Raffaele Paci & Jordy Suriñach & Raul Ramos & Jordi Suriñach, 2017. "A Gravity Model of Migration Between the ENC and the EU," Tijdschrift voor Economische en Sociale Geografie, Royal Dutch Geographical Society KNAG, vol. 108(1), pages 21-35, February.
    10. Grogger, Jeffrey & Hanson, Gordon H., 2011. "Income maximization and the selection and sorting of international migrants," Journal of Development Economics, Elsevier, vol. 95(1), pages 42-57, May.
    11. Michel Beine & Simone Bertoli & Jesús Fernández-Huertas Moraga, 2016. "A Practitioners’ Guide to Gravity Models of International Migration," The World Economy, Wiley Blackwell, vol. 39(4), pages 496-512, April.
    12. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," Post-Print hal-03470458, HAL.
    13. Michel Beine, 2016. "The role of networks for migration flows: an update," International Journal of Manpower, Emerald Group Publishing Limited, vol. 37(7), pages 1154-1171, October.
    14. repec:hal:spmain:info:hdl:2441/361levbcs399s9oa154em6h9jl is not listed on IDEAS
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    Cited by:

    1. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," SciencePo Working papers Main hal-03936221, HAL.
    2. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," Working Papers hal-03936221, HAL.

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    More about this item

    Keywords

    inverse optimal transport; coordinate descent; ISTA;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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