Bayesian Inference for Optimal Transport with Stochastic Cost

Loading...
Thumbnail Image

Access rights

openAccess

URL

Journal Title

Journal ISSN

Volume Title

A4 Artikkeli konferenssijulkaisussa

Date

2021

Major/Subject

Mcode

Degree programme

Language

en

Pages

16
1601-1616

Series

Proceedings of Asian Conference on Machine Learning, Proceedings of Machine Learning Research, Volume 157

Abstract

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

Description

Keywords

Other note

Citation

Mallasto, A, Heinonen, M & Kaski, S 2021, Bayesian Inference for Optimal Transport with Stochastic Cost . in Proceedings of Asian Conference on Machine Learning . Proceedings of Machine Learning Research, vol. 157, JMLR, pp. 1601-1616, Asian Conference on Machine Learning, Virtual, Online, 17/11/2021 . < https://proceedings.mlr.press/v157/mallasto21a/mallasto21a.pdf >