Related papers: Local Orthogonal Polynomial Expansion for Density …
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
We introduce a non-parametric density estimator deemed Radial Voronoi Density Estimator (RVDE). RVDE is grounded in the geometry of Voronoi tessellations and as such benefits from local geometric adaptiveness and broad convergence…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate…
We propose the periodic scaled Korobov kernel (PSKK) method for nonparametric density estimation on $\mathbb{R}^d$. By first wrapping the target density into a periodic version through modulo operation and subsequently applying kernel ridge…
In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
Open-set biometrics faces challenges with probe subjects who may not be enrolled in the gallery, as traditional biometric systems struggle to detect these non-mated probes. Despite the growing prevalence of multi-sample galleries in…
In this paper, we consider an infinite dimensional exponential family, $\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a…
We propose a flexible method for estimating luminosity functions (LFs) based on kernel density estimation (KDE), the most popular nonparametric density estimation approach developed in modern statistics, to overcome issues surrounding…
In this article we perform an asymptotic analysis of parallel Bayesian logspline density estimators. Such estimators are useful for the analysis of datasets that are partitioned into subsets and stored in separate databases without the…
This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can…
Explaining closed-source Large Language Model (LLM) outputs is challenging because API access prevents gradient-based attribution, while perturbation methods are costly and noisy when they depend on regenerated text. We introduce…
The probability density function (PDF) plays a central role in statistical and machine learning modeling. Real-world data often deviates from Gaussian assumptions, exhibiting skewness and exponential decay. To evaluate how well different…
The knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic ``perturbative'' equation of state of a homogeneous ultracold gas we make predictions…
The purpose of this paper is to investigate RBF approximation with highly nonuniform centers. Recently, DeVore and Ron have developed a notion of the local density of a set of centers -- a notion that permits precise pointwise error…
The local descriptors have gained wide range of attention due to their enhanced discriminative abilities. It has been proved that the consideration of multi-scale local neighborhood improves the performance of the descriptor, though at the…
Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…
Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…