Related papers: The Hellinger Correlation
A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…
We propose new summary measures of diagnostic test accuracy which can be used as companions to existing diagnostic accuracy measures. Conceptually, our summary measures are tantamount to the so-called Hellinger affinity and we show that…
The simplicity of a question such as wondering if correlations characterize or not a certain system collides with the experimental difficulty of accessing such information. Here we present a low demanding experimental approach which refers…
A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state {\rho} of a composite system AB as a probe for a quantum illumination task [e.g. see S. Lloyd, Science 321, 1463 (2008)], in…
Quantum measurements are crucial for quantum technologies and give rise to some of the most classically counter-intuitive quantum phenomena. As such, the ability to certify the presence of genuinely non-classical joint measurements in a…
The demonstration and use of Bell-nonlocality, a concept that is fundamentally striking and is at the core of applications in device independent quantum information processing, relies heavily on the assumption of measurement independence,…
Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum…
Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…
The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…
Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the…
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…
This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach…
Several performance measures can be used for evaluating classification results: accuracy, F-measure, and many others. Can we say that some of them are better than others, or, ideally, choose one measure that is best in all situations? To…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…
The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…
We show that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states. Specifically, spatially-separated parties who perform local measurements on a…