Bayesian Inference for Optimal Transport with Stochastic Cost

Anton Mallasto, Markus Heinonen, Samuel Kaski
Proceedings of The 13th Asian Conference on Machine Learning, PMLR 157:1601-1616, 2021.

Abstract

In machine learning and computer vision, optimal transport has had significant success inlearning generative models and defining metric distances between structured and stochasticdata objects, that can be cast as probability measures. The key element of optimal trans-port is the so called lifting of anexactcost (distance) function, defined on the sample space,to a cost (distance) between probability measures over the sample space. However, in manyreal life applications the cost isstochastic: e.g., the unpredictable traffic flow affects the costof transportation between a factory and an outlet. To take this stochasticity into account,we introduce a Bayesian framework for inferring the optimal transport plan distributioninduced by the stochastic cost, allowing for a principled way to include prior informationand to model the induced stochasticity on the transport plans. Additionally, we tailor anHMC method to sample from the resulting transport plan posterior distribution.

Cite this Paper

BibTeX
@InProceedings{pmlr-v157-mallasto21a, title = {Bayesian Inference for Optimal Transport with Stochastic Cost}, author = {Mallasto, Anton and Heinonen, Markus and Kaski, Samuel}, booktitle = {Proceedings of The 13th Asian Conference on Machine Learning}, pages = {1601--1616}, year = {2021}, editor = {Balasubramanian, Vineeth N. and Tsang, Ivor}, volume = {157}, series = {Proceedings of Machine Learning Research}, month = {17--19 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v157/mallasto21a/mallasto21a.pdf}, url = {https://proceedings.mlr.press/v157/mallasto21a.html}, abstract = {In machine learning and computer vision, optimal transport has had significant success inlearning generative models and defining metric distances between structured and stochasticdata objects, that can be cast as probability measures. The key element of optimal trans-port is the so called lifting of anexactcost (distance) function, defined on the sample space,to a cost (distance) between probability measures over the sample space. However, in manyreal life applications the cost isstochastic: e.g., the unpredictable traffic flow affects the costof transportation between a factory and an outlet. To take this stochasticity into account,we introduce a Bayesian framework for inferring the optimal transport plan distributioninduced by the stochastic cost, allowing for a principled way to include prior informationand to model the induced stochasticity on the transport plans. Additionally, we tailor anHMC method to sample from the resulting transport plan posterior distribution.} }
Endnote
%0 Conference Paper %T Bayesian Inference for Optimal Transport with Stochastic Cost %A Anton Mallasto %A Markus Heinonen %A Samuel Kaski %B Proceedings of The 13th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Vineeth N. Balasubramanian %E Ivor Tsang %F pmlr-v157-mallasto21a %I PMLR %P 1601--1616 %U https://proceedings.mlr.press/v157/mallasto21a.html %V 157 %X In machine learning and computer vision, optimal transport has had significant success inlearning generative models and defining metric distances between structured and stochasticdata objects, that can be cast as probability measures. The key element of optimal trans-port is the so called lifting of anexactcost (distance) function, defined on the sample space,to a cost (distance) between probability measures over the sample space. However, in manyreal life applications the cost isstochastic: e.g., the unpredictable traffic flow affects the costof transportation between a factory and an outlet. To take this stochasticity into account,we introduce a Bayesian framework for inferring the optimal transport plan distributioninduced by the stochastic cost, allowing for a principled way to include prior informationand to model the induced stochasticity on the transport plans. Additionally, we tailor anHMC method to sample from the resulting transport plan posterior distribution.
APA
Mallasto, A., Heinonen, M. & Kaski, S.. (2021). Bayesian Inference for Optimal Transport with Stochastic Cost. Proceedings of The 13th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 157:1601-1616 Available from https://proceedings.mlr.press/v157/mallasto21a.html.

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