相关论文: Sharp Large Deviations for empirical correlation c…
The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language…
In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which…
Spatial autocorrelation analysis is the basis for spatial autoregressive modeling. However, the relationships between spatial correlation coefficients and spatial regression models are not yet well clarified. The paper is devoted to explore…
The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian manifolds,…
In this article we study the Dyson Bessel process, which describes the evolution of singular values of rectangular matrix Brownian motions, and prove a large deviation principle for its empirical particle density. We then use it to obtain…
There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…
We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
The Pearson product-moment correlation coefficient (rp) and the Spearman rank correlation coefficient (rs) are widely used in psychological research. We compare rp and rs on 3 criteria: variability, bias with respect to the population…
We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and R\'enyi/Tsallis relative distances (including Pearson's…
We investigate the Large Deviations properties of bootstrapped empirical measure with exchangeable weights. Our main result shows in great generality how the resulting rate function combines the LD properties of both the sample weights and…
Large deviation estimates for the following linear parabolic equation are studied: \[ \frac{\partial u}{\partial t}=\tr\Big(a(x)D^2u\Big) + b(x)\cdot D u + \int_{\R^N} \Big\{(u(x+y)-u(x)-(D u(x)\cdot y)\ind{|y|<1}(y)\Big\}\d\mu(y), \] where…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
Presented is an inductive formula for computing the sample moments of the distribution of Pearson's sample correlation over permutation of data. These exact formulas for the sample moments suggest the possibility of more precise and…
In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…
The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…
Pearson's correlation is an important summary measure of the amount of dependence between two variables. It is natural to want to generalise the concept of correlation as a single number that measures the inter-relatedness of three or more…
Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…
The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.