SISTA: Learning Optimal Transport Costs under Sparsity Constraints

Guillaume Carlier, Arnaud Dupuy (), Alfred Galichon () and Yifei Sun
Additional contact information
Guillaume Carlier: Université Paris-Dauphine
Alfred Galichon: New York University
Yifei Sun: New York University

No 14397, IZA Discussion Papers from Institute of Labor Economics (IZA)

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.

Keywords: coordinate descent; inverse optimal transport; ISTA (search for similar items in EconPapers)
JEL-codes: C2 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2021-05
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published - published in: Communication on Pure and Applied Mathematics, 2023, 76 (9), 1659-1677

Downloads: (external link)
https://docs.iza.org/dp14397.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:iza:izadps:dp14397

Ordering information: This working paper can be ordered from
IZA, Margard Ody, P.O. Box 7240, D-53072 Bonn, Germany

Access Statistics for this paper

More papers in IZA Discussion Papers from Institute of Labor Economics (IZA) IZA, P.O. Box 7240, D-53072 Bonn, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Holger Hinte ().