相关论文: Self-consistent distance determinations for Lutz-K…

The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in…

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying…

Accurate and precise astronomical distance determinations are crucial for derivations of, among others, the masses and luminosities of a large variety of distant objects. Astronomical distance determination has traditionally relied on the…

To determine the local dark matter density (LDMD) of the solar system is a classical problem in astronomy. Recently, a novel method of determining the LDMD from stellar distribution and vertical velocity dispersion profiles perpendicular to…

We provide a simple $C^{1,1}$ approximation of the squared Wasserstein distance on R^d when one of the two measures is fixed. This approximation converges locally uniformly. More importantly, at points where the differential of the squared…

We derive Bayesian distances for all stars in the RV sample of Gaia DR2, and use the statistical method of Schoenrich, Binney & Asplund(2012) to validate the distances and test the Gaia parallaxes. In contrast to other methods, which rely…

This paper presents a cross-calibrated catalog of Hipparcos and Gaia astrometry to enable their use in measuring changes in proper motion, i.e., accelerations in the plane of the sky. The final catalog adopts the reference frame of the…

We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio…

The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…

Log-Euclidean distances are commonly used to quantify the similarity between positive definite matrices using geometric considerations. This paper analyzes the behavior of this distance when it is used to measure closeness between…

Near-future data from ESA's Gaia mission will provide precise, full phase-space information for hundreds of millions of stars out to heliocentric distances of ~10 kpc. This "horizon" for full phase-space measurements is imposed by the Gaia…

A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric.…

Astrometric surveys such as Gaia and LSST will measure parallaxes for hundreds of millions of stars. Yet they will not measure a single distance. Rather, a distance must be estimated from a parallax. In this didactic article, I show that…

In recent study in Ref.[7] (arXiv: 2401.12525), we have introduced a method aimed at calculating the weak-field asymptotic deflection angle. This method offers an efficient computational approach that avoids the complexities of integration…

We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically…

The Hipparcos data allow a major step forward in the research of `moving groups' in the Solar neighbourhood, as the common motion of group members causes converging proper motions. Previous knowledge on these coherent structures in velocity…

In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…

We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…

In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the medial axis and relate it to a path-based adaptive metric on…

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…