Related papers: A note on distance variance for categorical variab…
This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…
The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
Quantifying degrees of fusion and separability between data groups in representation space is a fundamental problem in representation learning, particularly under domain shift. A meaningful metric should capture fusion-altering factors like…
Missingness and measurement frequency are two sides of the same coin. How frequent should we measure clinical variables and conduct laboratory tests? It depends on many factors such as the stability of patient conditions, diagnostic…
Researchers have developed ways to generalize the mean and variance to situations in which a data metric is available. We apply the tools developed in Pennec (2006) to categorical data, and show the generality of this approach by…
We are interested in comparing probability distributions defined on Riemannian manifold. The traditional approach to study a distribution relies on locating its mean point and finding the dispersion about that point. On a general manifold…
Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…
Past research relates design creativity to 'divergent thinking,' i.e., how well the concept space is explored during the early phase of design. Researchers have argued that generating several concepts would increase the chances of producing…
The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in $[0,1]$. This distance plays a fundamental role in machine learning and signal…
Popular measures of meta-analysis heterogeneity, such as $I^2$, cannot be considered measures of population heterogeneity since they are dependant on samples sizes within studies. The coefficient of variation (CV) recently introduced and…
We establish quantitative comparisons between classical distances for probability distributions belonging to the class of convex probability measures. Distances include total variation distance, Wasserstein distance, Kullback-Leibler…
We propose the Variation Calibration Error (VCE) metric for assessing the calibration of machine learning classifiers. The metric can be viewed as an extension of the well-known Expected Calibration Error (ECE) which assesses the…
One of the key issues in quantum information theory related problems concerns with that of distinguishability of quantum states. In this context, Bures distance serves as one of the foremost choices among various distance measures. It also…
We propose a covariant and geometric framework to introduce space distances as they are used by astronomers. In particular, we extend the definition of space distances from the one used between events to non-test-bodies with horizons and…
In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample…
Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic…
The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analogs…