Related papers: Sharp Anti-Concentration Inequalities for Extremum…
We study the $L^p$ concentration problem for the Born--Jordan distribution in dimension $d>1$, thus extending the one-dimensional analysis in [Stra-Svela-Trapasso, J. Math. Pures Appl. (2026)]. We show that the existence of concentration…
Under the high-dimensional setting that data dimension and sample size tend to infinity proportionally, we derive the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix. Different…
We consider a random variable $X$ that takes values in a (possibly infinite-dimensional) topological vector space $\mathcal{X}$. We show that, with respect to an appropriate "normal distance" on $\mathcal{X}$, concentration inequalities for…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…
Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but the corresponding problem of proving lower bounds for this task has remained elusive, with lower bounds previously known only in dimension one. In this…
In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases…
We investigate concentration properties of functions of random vectors with values in the discrete cube, satisfying the stochastic covering property (SCP) or the strong Rayleigh property (SRP). Our result for SCP measures include…
Copulas are powerful statistical tools for capturing dependencies across data dimensions. Applying Copulas involves estimating independent marginals, a straightforward task, followed by the much more challenging task of determining a single…
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
A central problem in machine learning and statistics is to model joint densities of random variables from data. Copulas are joint cumulative distribution functions with uniform marginal distributions and are used to capture…
Making use of the total variation of particular functions, we give an explicit formula for the pointwise supremum of the set of all copulas with a given curvilinear section. When the pointwise supremum is a copula is characterized. We also…
We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…
For extreme value copulas with a known upper tail dependence coefficient we find pointwise upper and lower bounds, which are used to establish upper and lower bounds of the Spearman and Kendall correlation coefficients. We shown that in all…
Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to…
Neural networks excel at discovering statistical patterns in high-dimensional data sets. In practice, higher-order cumulants, which quantify the non-Gaussian correlations between three or more variables, are particularly important for the…
In this paper we present a surprisingly general extension of the main result of a paper that appeared in this journal: I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48--66. The main tools we…
We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…