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Stuart, Andrew M. and Wolfram, Marie-Therese (2020) Inverse optimal transport. SIAM Journal on Applied Mathematics, 80 (1). pp. 599-619. doi:10.1137/19M1261122 ISSN 0036-1399.
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Official URL: https://doi.org/10.1137/19M1261122
Abstract
Discrete optimal transportation problems arise in various contexts in engineering, the sciences, and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted by noise. In this paper we propose a systematic approach to infer unknown costs from noisy observations of optimal transportation plans. The algorithm requires only the ability to solve the forward optimal transport problem, which is a linear program, and to generate random numbers. It has a Bayesian interpretation and may also be viewed as a form of stochastic optimization. We illustrate the developed methodologies using the example of international migration flows. Reported migration flow data captures (noisily) the number of individuals moving from one country to another in a given period of time. It can be interpreted as a noisy observation of an optimal transportation map, with costs related to the geographical position of countries. We use a graph-based formulation of the problem, with countries at the nodes of graphs and nonzero weighted adjacencies only on edges between countries which share a border. We use the proposed algorithm to estimate the weights, which represent cost of transition, and to quantify uncertainty in these weights.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | SIAM Journal on Applied Mathematics | ||||||
| Publisher: | Society for Industrial and Applied Mathematics | ||||||
| ISSN: | 0036-1399 | ||||||
| Official Date: | 25 February 2020 | ||||||
| Dates: |
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| Volume: | 80 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 599-619 | ||||||
| DOI: | 10.1137/19M1261122 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | First Published in [Publication] in [volume and number, or year], published by the Society for Industrial and Applied Mathematics (SIAM) Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | © 2020, Society for Industrial and Applied Mathematics | ||||||
| Date of first compliant deposit: | 6 December 2019 | ||||||
| Date of first compliant Open Access: | 11 March 2020 | ||||||
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