Related papers: Restoring Wasserstein Rigidity with a single point
In this article, we present some fixed point theorems in partially ordered G-metric space using the concept of $(\psi,\phi)$- weak contraction which extend many existing fixed point theorems in such space. We also give some examples to show…
We investigate the stability of the Wasserstein distance, a metric structure on the space of probability measures arising from the theory of optimal transport, under metric ultralimits. We first show that if $(X_{i},d_{i})_{i\in\mathbb{N}}$…
We study several rigidity properties of $p$-adic local systems on a smooth rigid analytic space $X$ over a $p$-adic field. We prove that the monodromy of the log isocrystal attached to a $p$-adic local system is ''rigid'' along irreducible…
Quantum Wasserstein divergences are modified versions of quantum Wasserstein distances defined by channels, and they are conjectured to be genuine metrics on quantum state spaces by De Palma and Trevisan. We prove triangle inequality for…
In this paper, we propose a new method to measure the probabilistic robustness of stochastic jump linear system with respect to both the initial state uncertainties and the randomness in switching. Wasserstein distance which defines a…
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…
This paper primarily considers the robust estimation problem under Wasserstein distance constraints on the parameter and noise distributions in the linear measurement model with additive noise, which can be formulated as an…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
We study the geometric structure of the space of random measures $\mathcal{P}_p(\mathcal{P}_p(X))$, endowed with the Wasserstein on Wasserstein metric, where $(X, d)$ is a complete separable metric space. In this setting, we prove a metric…
Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…
This paper investigates a time discrete variational model for splines in Wasserstein spaces to interpolate probability measures. Cubic splines in Euclidean space are known to minimize the integrated squared acceleration subject to a set of…
The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…
The convergence rate in Wasserstein distance is estimated for the empirical measures of symmetric semilinear SPDEs. Unlike in the finite-dimensional case that the convergence is of algebraic order in time, in the present situation the…
This paper introduces the concept of quasi $\alpha$-firmly nonexpansive mappings in Wasserstein spaces over $\mathbb R^d$ and analyzes properties of these mappings. We prove that for quasi $\alpha$-firmly nonexpansive mappings satisfying a…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
In this paper, we consider some rigidity results for the Einstein metrics as the critical points of some known quadratic curvature functionals on complete manifolds, characterized by some point-wise inequalities. Moreover, we also provide…
We study the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in computing the Wasserstein barycenter of $m$ discrete probability measures supported on a finite metric space of size $n$. We show first that the…
Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…
We analyze theoretically complete wetting of a substrate supporting an array of parallel, vertical plates which can tilt elastically. The adsorbed liquid tilts the plates, inducing clustering, and thus modifies the substrate geometry. In…