Article (Scientific journals)
SISTA: Learning Optimal Transport Costs under Sparsity Constraints
Dupuy, Arnaud; Carlier, Guillaume; Galichon, Alfred et al.
In pressIn Communications on Pure and Applied Mathematics
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Keywords :
: inverse optimal transport, coordinate descent, ISTA
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
Dupuy, Arnaud ;  University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Department of Economics and Management (DEM)
Carlier, Guillaume
Galichon, Alfred
Sun, Yifei
External co-authors :
yes
Language :
English
Title :
SISTA: Learning Optimal Transport Costs under Sparsity Constraints
Publication date :
In press
Journal title :
Communications on Pure and Applied Mathematics
ISSN :
1097-0312
Publisher :
John Wiley & Sons, Hoboken, United States - New Jersey
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
Available on ORBilu :
since 04 January 2021

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