Discrete Probabilistic Inverse Optimal Transport

Wei-Ting Chiu, Pei Wang, Patrick Shafto
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:3925-3946, 2022.

Abstract

Inverse Optimal Transport (IOT) studies the problem of inferring the underlying cost that gives rise to an observation on coupling two probability measures. Couplings appear as the outcome of matching sets (e.g. dating) and moving distributions (e.g. transportation). Compared to Optimal transport (OT), the mathematical theory of IOT is undeveloped. We formalize and systematically analyze the properties of IOT using tools from the study of entropy-regularized OT. Theoretical contributions include characterization of the manifold of cross-ratio equivalent costs, the implications of model priors, and derivation of an MCMC sampler. Empirical contributions include visualizations of cross-ratio equivalent effect on basic examples, simulations validating theoretical results and experiments on real world data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-chiu22b, title = {Discrete Probabilistic Inverse Optimal Transport}, author = {Chiu, Wei-Ting and Wang, Pei and Shafto, Patrick}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {3925--3946}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/chiu22b/chiu22b.pdf}, url = {https://proceedings.mlr.press/v162/chiu22b.html}, abstract = {Inverse Optimal Transport (IOT) studies the problem of inferring the underlying cost that gives rise to an observation on coupling two probability measures. Couplings appear as the outcome of matching sets (e.g. dating) and moving distributions (e.g. transportation). Compared to Optimal transport (OT), the mathematical theory of IOT is undeveloped. We formalize and systematically analyze the properties of IOT using tools from the study of entropy-regularized OT. Theoretical contributions include characterization of the manifold of cross-ratio equivalent costs, the implications of model priors, and derivation of an MCMC sampler. Empirical contributions include visualizations of cross-ratio equivalent effect on basic examples, simulations validating theoretical results and experiments on real world data.} }
Endnote
%0 Conference Paper %T Discrete Probabilistic Inverse Optimal Transport %A Wei-Ting Chiu %A Pei Wang %A Patrick Shafto %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-chiu22b %I PMLR %P 3925--3946 %U https://proceedings.mlr.press/v162/chiu22b.html %V 162 %X Inverse Optimal Transport (IOT) studies the problem of inferring the underlying cost that gives rise to an observation on coupling two probability measures. Couplings appear as the outcome of matching sets (e.g. dating) and moving distributions (e.g. transportation). Compared to Optimal transport (OT), the mathematical theory of IOT is undeveloped. We formalize and systematically analyze the properties of IOT using tools from the study of entropy-regularized OT. Theoretical contributions include characterization of the manifold of cross-ratio equivalent costs, the implications of model priors, and derivation of an MCMC sampler. Empirical contributions include visualizations of cross-ratio equivalent effect on basic examples, simulations validating theoretical results and experiments on real world data.
APA
Chiu, W., Wang, P. & Shafto, P.. (2022). Discrete Probabilistic Inverse Optimal Transport. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:3925-3946 Available from https://proceedings.mlr.press/v162/chiu22b.html.

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