Bayesian Inference for Optimal Transport with Stochastic Cost

by   Anton Mallasto, et al.

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.



page 1

page 2

page 3

page 4


BoMb-OT: On Batch of Mini-batches Optimal Transport

Mini-batch optimal transport (m-OT) has been successfully used in practi...

HINT: Hierarchical Invertible Neural Transport for General and Sequential Bayesian inference

In this paper, we introduce Hierarchical Invertible Neural Transport (HI...

Depth profiles and the geometric exploration of random objects through optimal transport

We propose new tools for the geometric exploration of data objects takin...

Transport away your problems: Calibrating stochastic simulations with optimal transport

Stochastic simulators are an indispensable tool in many branches of scie...

Hypergraph Co-Optimal Transport: Metric and Categorical Properties

Hypergraphs capture multi-way relationships in data, and they have conse...

Optimal transport in multilayer networks

Modeling traffic distribution and extracting optimal flows in multilayer...

𝒲_∞-transport with discrete target as a combinatorial matching problem

In this short note, we show that given a cost function c, any coupling π...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.