Related papers: Bayesian Inference for Optimal Transport with Stoc…
This paper introduces a novel motion planning algorithm for stochastic scenarios. We extend the concept of a navigation function to such scenarios. Our main idea is to consider both the Gaussian distribution probabilities of the players'…
The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a…
In this paper, we address the problem of sampling-based motion planning under motion and measurement uncertainty with probabilistic guarantees. We generalize traditional sampling-based tree-based motion planning algorithms for deterministic…
Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
The costs incurred in a mobile robot (MR) change due to change in physical and environmental factors. Usually, there are two approaches to consider these costs, either explicitly modelling these different factors to calculate the cost or…
The two-stage stochastic unit commitment problem has become an important tool to support decision-making under uncertainty in power systems. Representing the uncertainty by a large number of scenarios guarantees accurate results but…
Controlling the $\mathcal W_\infty$ Wasserstein distance by the $\mathcal W_p$ Wasserstein distance is interesting both for theorical and numerical applications. A first paper on this problem was written several years ago [3]. Some year…
This paper introduces the first statistically consistent estimator of the optimal transport map between two probability distributions, based on neural networks. Building on theoretical and practical advances in the field of Lipschitz neural…
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of…
This paper proposes a generalised framework for density estimation in large networks with measurable spatiotemporal variance in edge weights. We solve the stochastic shortest path problem for a large network by estimating the density of the…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to…
We give a statistical interpretation of entropic optimal transport by showing that performing maximum-likelihood estimation for Gaussian deconvolution corresponds to calculating a projection with respect to the entropic optimal transport…
We research relations between optimal transport theory (OTT) and approximate Bayesian computation (ABC) possibly connected to relevant metrics defined on probability measures. Those of ABC are computational methods based on Bayesian…
Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In…
Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in…