• Corpus ID: 224705969

Bayesian Inference for Optimal Transport with Stochastic Cost

@inproceedings{Mallasto2021BayesianIF,
  title={Bayesian Inference for Optimal Transport with Stochastic Cost},
  author={Anton Mallasto and Markus Heinonen and Samuel Kaski},
  booktitle={ACML},
  year={2021}
}
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 \emph{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… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 37 REFERENCES
Stochastic Optimization for Large-scale Optimal Transport
TLDR
A new class of stochastic optimization algorithms to cope with large-scale problems routinely encountered in machine learning applications, based on entropic regularization of the primal OT problem, which results in a smooth dual optimization optimization which can be addressed with algorithms that have a provably faster convergence.
Tsallis Regularized Optimal Transport and Ecological Inference
TLDR
The first application of optimal transport to the problem of ecological inference, that is, the reconstruction of joint distributions from their marginals, is presented, a problem of large interest in the social sciences.
Variational Inference: A Review for Statisticians
TLDR
Variational inference (VI), a method from machine learning that approximates probability densities through optimization, is reviewed and a variant that uses stochastic optimization to scale up to massive data is derived.
Minibatch optimal transport distances; analysis and applications
TLDR
It is argued that the minibatch strategy comes with appealing properties such as unbiased estimators, gradients and a concentration bound around the expectation, but also with limits: theminibatch OT is not a distance.
Optimal Transport for Gaussian Mixture Models
TLDR
An optimal mass transport framework on the space of Gaussian mixture models as a submanifold of probability densities equipped with the Wasserstein metric is introduced, which provides natural ways to compare, interpolate, and average Gaussia mixture models.
Quadratically Regularized Optimal Transport
We investigate the problem of optimal transport in the so-called Kantorovich form, i.e. given two Radon measures on two compact sets, we seek an optimal transport plan which is another Radon measure
A Complete Recipe for Stochastic Gradient MCMC
TLDR
This paper provides a general recipe for constructing MCMC samplers--including stochastic gradient versions--based on continuous Markov processes specified via two matrices, and uses the recipe to straightforwardly propose a new state-adaptive sampler: stochastics gradient Riemann Hamiltonian Monte Carlo (SGRHMC).
Sinkhorn Distances: Lightspeed Computation of Optimal Transport
TLDR
This work smooths the classic optimal transport problem with an entropic regularization term, and shows that the resulting optimum is also a distance which can be computed through Sinkhorn's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transport solvers.
Computational Optimal Transport: With Applications to Data Science
TLDR
Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes.
Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review
TLDR
This article will discuss how a generalization of the reinforcement learning or optimal control problem, which is sometimes termed maximum entropy reinforcement learning, is equivalent to exact probabilistic inference in the case of deterministic dynamics, and variational inference inThe case of stochastic dynamics.
...
...