Related papers: Bernstein-type approximation of set-valued functio…
The weighted Selberg integral is a discrete mean-square, that is a generalization of the classical Selberg integral of primes to an arithmetic function $f$, whose values in a short interval are suitably attached to a weight function. We…
The emergence of time-series foundation model research elevates the growing need to measure the (dis)similarity of time-series datasets. A time-series dataset similarity measure aids research in multiple ways, including model selection,…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…
Based on the assumption of the existence and uniqueness of the invariant measure for McKean-Vlasov stochastic differential equations (MV-SDEs), a self-interacting process that depends only on the current and historical information of the…
The support vector machines (SVM) is a powerful classifier used for binary classification to improve the prediction accuracy. However, the non-differentiability of the SVM hinge loss function can lead to computational difficulties in high…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
The major contributions of this paper lie in two aspects. Firstly, we focus on deriving Bernstein-type inequalities for both geometric and algebraic irregularly-spaced NED random fields, which contain time series as special case.…
In [14,26], new approximation classes of self-referential functions are introduced as fractal versions of the classes of polynomials and rational functions. As a sequel, in the present article, we define a new approximation class consisting…
The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the…
Time series analysis of fMRI data is an important area of medical statistics for neuroimaging data. The neuroimaging community has embraced mean-field variational Bayes (VB) approximations, which are implemented in Statistical Parametric…
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…
Given a Hilbert space $\mathcal H$ and a finite measure space $\Omega$, the approximation of a vector-valued function $f: \Omega \to \mathcal H$ by a $k$-dimensional subspace $\mathcal U \subset \mathcal H$ plays an important role in…
This article presents an improved approximation for the effective degrees of freedom in the Satterthwaite (1941, 1946) method which estimates the distribution of a weighted combination of variance components The standard Satterthwaite…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert…
We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals…
We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced…