Related papers: Generalized differentiation in Wasserstein space a…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
The duality in Bakry-\'Emery's gradient estimates and Wasserstein controls for heat distributions is extended to that in refined estimates in a high generality. As a result, we find an equivalent condition to Bakry-Ledoux's refined gradient…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
Generalizations of the Weierstrass formulae to generic surface immersed into $R^4$, $S^4$ and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation…
We derive quantitative bounds on the rate of convergence in $L^1$ Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the number of observations. We focus on situations where the…
The Wasserstein metric is introduced as a probabilistic method to enable quantitative evaluations of LES combustion models. The Wasserstein metric can directly be evaluated from scatter data or statistical results using probabilistic…
We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
Let $M$ be a complete connected Riemannian manifold. For $n \geq 0$, we endow the Wasserstein space $P^{(n)}_2(M) = P_2(\ldots P_2(M)\ldots)$, equipped with the Wasserstein distance $W_2$, with a variational structure that generalizes the…
In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming…
Precise control under uncertainty requires a good understanding and characterization of the noise affecting the system. This paper studies the problem of steering state distributions of dynamical systems subject to partially known…
In this paper, particle physics concepts are blended into a field theory for macroscopic phenomena: Fluid mechanics is enhanced by anticommuting Grassmann variables to describe vorticity, while an additional interaction for the Grassmann…
We consider a mean-field control problem in which admissible controls are required to be adapted to the common noise filtration. The main objective is to show how the mean-field control problem can be approximates by time consistent…
We present a methodology for predictable and safe covariance steering control of uncertain nonlinear stochastic processes. The systems under consideration are subject to general uncertainties, which include unbounded random disturbances…
We propose a distributionally robust classification model with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at…
In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general…
We consider multiperiod stochastic control problems with non-parametric uncertainty on the underlying probabilistic model. We derive a new metric on the space of probability measures, called the adapted $(p, \infty)$--Wasserstein distance…
In this paper, we establish the evolution variational inequality for the weighted Wasserstein distance, without assuming convexity of domains. Thanks to this evolution variational inequality, we can carry out some arguments with weighted…
We study the regularity properties of integro-partial differential equations of Hamilton-Jocobi-Bellman type with terminal condition, which can be interpreted through a stochastic control system, composed of a forward and a backward…
We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data. We use the Wasserstein-2 geometry to capture semantically meaningful neighborhoods in the space of images, and…