Related papers: Universal kernel-type estimation of random fields

We constuct a sequential adaptive procedure for estimating the autoregressive function at a given point in nonparametric autoregression models with Gaussian noise. We make use of the sequential kernel estimators. The optimal adaptive…

It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…

Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…

Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity…

We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We…

Neural Networks (NNs) have been extensively used for a wide spectrum of real-world regression tasks, where the goal is to predict a numerical outcome such as revenue, effectiveness, or a quantitative result. In many such tasks, the point…

Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels…

This paper studies inference in predictive quantile regressions when the predictive regressor has a near-unit root. We derive asymptotic distributions for the quantile regression estimator and its heteroskedasticity and autocorrelation…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…

We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

We propose and study kernel conjugate gradient methods (KCGM) with random projections for least-squares regression over a separable Hilbert space. Considering two types of random projections generated by randomized sketches and Nystr\"{o}m…

We present \textit{universal} estimators for the statistical mean, variance, and scale (in particular, the interquartile range) under pure differential privacy. These estimators are universal in the sense that they work on an arbitrary,…

In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…

Route alignment design in surveying and transportation engineering frequently involves fixed waypoint constraints, where a path must precisely traverse specific coordinates. While existing literature primarily relies on geometric…

The recent discovery of the equivalence between infinitely wide neural networks (NNs) in the lazy training regime and Neural Tangent Kernels (NTKs) (Jacot et al., 2018) has revived interest in kernel methods. However, conventional wisdom…

While both classical and neural network classifiers can achieve high accuracy, they fall short on offering uncertainty bounds on their predictions, making them unfit for safety-critical applications. Existing kernel-based classifiers that…