Related papers: Measuring deviations from spherical symmetry
The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…
The validation of global climate models is crucial to ensure the accuracy and efficacy of model output. We introduce the spherical convolutional Wasserstein distance to more comprehensively measure differences between climate models and…
We generalize the Jensen-Shannon divergence by considering a variational definition with respect to a generic mean extending thereby the notion of Sibson's information radius. The variational definition applies to any arbitrary distance and…
The conceptualization of space is crucial for comprehending the processes that shape geographic phenomena. Functional space exhibits asymmetric spatial separations, which deviate from the symmetry axiom of metric space commonly adopted as a…
In this paper we deal with the problem of testing for the quality of $k$ probability distributions. We introduce a generalization of the maximum mean discrepancy that permits to characterize the null hypothesis. Then, an estimator of it is…
We consider two symmetry metrics commonly used to analyze partisan gerrymandering: the Mean-Median Difference (MM) and Partisan Bias (PB). Our main results compare, for combinations of seats and votes achievable in districted elections, the…
Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed. In…
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…
We report the discovery of an unexpected symmetry that correlates the spin of all elementary particles (integer versus half-integer) with the geographic location of their initial discovery. We find that this correlation is apparently…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
In this work we study the problem of single-shot discrimination of von Neumann measurements, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
In this paper, we consider the problem of estimating the distance between any two large data streams in small- space constraint. This problem is of utmost importance in data intensive monitoring applications where input streams are…
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…
The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…
In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…
This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…
In this paper, we aim to provide a statistical theory for object matching based on the Gromov-Wasserstein distance. To this end, we model general objects as metric measure spaces. Based on this, we propose a simple and efficiently…