相关论文: The affinely invariant distance correlation

A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…

We investigate ergodic-theoretical quantities and large deviation properties of one-dimensional intermittent maps, that have not only an indifferent fixed point but also a singular structure such that the uniform measure is invariant under…

Atar, Chowdhary and Dupuis have recently exhibited a variational formula for exponential integrals of bounded measurable functions in terms of R\'enyi divergences. We develop a variational characterization of the R\'enyi divergences between…

In statistical analysis, measuring a score of predictive performance is an important task. In many scientific fields, appropriate scores were tailored to tackle the problems at hand. A proper score is a popular tool to obtain statistically…

We show that the covariant derivative of a spinor for a general affine connection, not restricted to be metric compatible, is given by the Fock-Ivanenko coefficients with the antisymmetric part of the Lorentz connection. The projective…

A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…

We introduce some new indexes to measure the departure of any multivariate continuous distribution on non-negative orthant from a given reference one such the uncorrelated exponential model, similar to the relative Fisher dispersion indexes…

The Interplanetary Magnetic Field shows complex spatial and temporal variations. Single spacecraft measurements reveal only a one dimensional section of this rich four dimensional phenomenon. Multi-point measurements of the four Cluster…

We consider the joint distribution of eigenvalue clusters of the Wigner ensemble separated by macroscopic distances (i.e., on the same scale as the difference between the edges of the semicircle law). We prove that under an averaging…

Approximate expressions for correlation functions in binary inhomogeneous mixtures are derived in a framework of the mesoscopic theory [Ciach A., Mol. Phys., 2011, {\textbf{109}}, 1101]. Fluctuation contribution is taken into account in a…

In this paper, we deal with the problem of inferring causal directions when the data is on discrete domain. By considering the distribution of the cause $P(X)$ and the conditional distribution mapping cause to effect $P(Y|X)$ as independent…

We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light…

We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…

Markov chains arising from random iteration of functions $S_{\theta}:X\to X$, $\theta \in \Theta$, where $X$ is a Polish space and $\Theta$ is arbitrary set of indices are considerd. At $x\in X$, $\theta$ is sampled from distribution…

We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…

Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…

The aim of this paper is to explore the relationship between invariant cones and nonlinear normal modes in piecewise linear mechanical systems. As a key result, we extend the invariant cone concept, originally established for homogeneous…

In this paper we propose and study a class of nonparametric, yet interpretable measures of association between two random vectors $X$ and $Y$ taking values in $\mathbb{R}^{d_1}$ and $\mathbb{R}^{d_2}$ respectively ($d_1, d_2\ge 1$). These…

A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…

Generalization and invariance are two essential properties of any machine learning model. Generalization captures a model's ability to classify unseen data while invariance measures consistency of model predictions on transformations of the…