Related papers: Optimal Confidence Band for Kernel Gradient Flow E…

Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…

This paper considers a canonical problem in kernel regression: how good are the model performances when it is trained by the popular online first-order algorithms, compared to the offline ones, such as ridge and ridgeless regression? In…

In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…

A standard approach to confidence intervals for quantiles requires good estimates of the quantile density. The optimal bandwidth for kernel estimation of the quantile density depends on an underlying location-scale family only through the…

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…

We provide uniform convergence rates for kernel averages on $[0,1]$ under equally-spaced fixed design points of the form $x_{t,T}=t/T,\ t\in\{1,\dotsc, T\},\ T\in\mathbb{N}$. The rates of weak and strong uniform consistency are derived…

The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of…

We show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the…

The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…

Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…

In this paper we establish the uniform in bandwidth consistency for the transformation kernel estimator of copulas introduced in [Omelka et al.(2009)]. To this end, we first prove a uniform in bandwidth law of the iterated logarithm for the…

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation…

Band-limited functions are fundamental objects that are widely used in systems theory and signal processing. In this paper we refine a recent nonparametric, nonasymptotic method for constructing simultaneous confidence regions for…

We study the kernelized bandit problem, that involves designing an adaptive strategy for querying a noisy zeroth-order-oracle to efficiently learn about the optimizer of an unknown function $f$ with a norm bounded by $M<\infty$ in a…

Given an i.i.d sample $(Y_i,Z_i)$, taking values in $\RRR^{d'}\times \RRR^d$, we consider a collection Nadarya-Watson kernel estimators of the conditional expectations $\EEE(<c_g(z),g(Y)>+d_g(z)\mid Z=z)$, where $z$ belongs to a compact set…

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel…

Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…

We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya-Watson regression estimator and the conditional empirical process. Our…

We are interested in the kernel of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both semidiscrete…