A research paper co-written by Prof. Arnaud Dupuy, professor within the Department of Economics at the Faculty of Law, Economics and Finance, has recently been accepted for publication in the review Communications on Pure and Applied Mathematics, a Q1-ranked journal by SJR.
Co-authored by Guillaume Carlier (Université Paris IX Dauphine), Alfred Galichon (New York University, Sciences Po) and Yifei Sun (New York University) the paper, titled “SISTA: Learning Optimal Transport Costs Under Sparsity Constraints”, describes, tests and applies a new algorithm called SISTA in order 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. It naturally extends the Sinkhorn algorithm which is a coordinate descent algorithm with respect to the transport potentials, for a fixed value of the parameter vector. One important advantage of the Sinkhorn algorithm compared with alternative methods is that it is fast, parameteter-free and can be naturally parallelized. In their paper, the researchers prove that the SISTA method converges linearly, illustrating through simulated examples that it is significantly faster than both coordinate descent and proximal gradient descent models.
The researchers then applied the SISTA method to estimating a model of migration, which predicts the flow of migrants using country-specific characteristics and pairwise measures of dissimilarity between countries. In the application of predicting bilateral migration flows, SISTA allowed researchers to learn which measures of dissimilarity between an origin and a destination country are the most important ones. Researchers ultimately discovered critical predictors of bilateral migrations flows, i.e., the interaction between the areas of the origin and destination countries, the interaction between the share of urban population that has access to improved sanitation facilities, and the interaction between the female life expectancy at birth in the origin and destination countries, that have been absent from literature on the subject.
The idea underlying the SISTA algorithm is broadly applicable and demonstrates the effectiveness of machine learning in quantitative social sciences. The same technique could be applied to predicting bilateral trade flows, the matching of workers to jobs, men to women, children to schools, etc. In all these applications, there exists a long list of attributes/characteristics upon which measures of dissimilarity between countries of origin and countries of destination, men and women, workers and jobs, can be constructed and could explain flows or matches. The researchers’ approach allows one to select those that matter the most.