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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.
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.
Original language  English 

Title of host publication  Proceedings of Asian Conference on Machine Learning 
Publisher  JMLR 
Pages  16011616 
Number of pages  16 
Publication status  Published  2021 
MoE publication type  A4 Conference publication 
Event  Asian Conference on Machine Learning  Virtual, Online Duration: 17 Nov 2021 → 19 Nov 2021 Conference number: 13 
Publication series
Name  Proceedings of Machine Learning Research 

Publisher  PMLR 
Volume  157 
ISSN (Electronic)  26403498 
Conference
Conference  Asian Conference on Machine Learning 

Abbreviated title  ACML 
City  Virtual, Online 
Period  17/11/2021 → 19/11/2021 
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Heinonen Markus ATpalkka: Deep learning with differential equations
01/09/2020 → 31/08/2025
Project: Academy of Finland: Other research funding

: Bridging the Reality Gap in Autonomous Learning
Kaski, S., Filstroff, L., Hämäläinen, A., Khoshvishkaie, A., Kulkarni, T. & Mallasto, A.
01/01/2020 → 31/12/2022
Project: Academy of Finland: Other research funding

Interactive machine learning from multiple biodata sources
Kaski, S., Hämäläinen, A., Gadd, C., Hegde, P., Shen, Z., Siren, J., Trinh, T., Jain, A. & Jälkö, J.
01/01/2019 → 31/08/2021
Project: Academy of Finland: Other research funding