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Related papers: Uniform convergence for Gaussian kernel ridge regr…

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We consider learning an unknown target function $f_*$ using kernel ridge regression (KRR) given i.i.d. data $(u_i,y_i)$, $i\leq n$, where $u_i \in U$ is a covariate vector and $y_i = f_* (u_i) +\varepsilon_i \in \mathbb{R}$. A recent string…

Machine Learning · Statistics 2024-03-15 Theodor Misiakiewicz , Basil Saeed

In this manuscript we consider Kernel Ridge Regression (KRR) under the Gaussian design. Exponents for the decay of the excess generalization error of KRR have been reported in various works under the assumption of power-law decay of…

Machine Learning · Statistics 2022-11-29 Hugo Cui , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

The anisotropic kernel ridge regression (AKRR) approach in nuclear mass predictions is developed by introducing the anisotropic kernel function into the kernel ridge regression (KRR) approach, without introducing new weight parameter or…

Nuclear Theory · Physics 2024-05-02 X. H. Wu , C. Pan

I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select…

Econometrics · Economics 2022-08-24 Rahul Singh

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…

Statistics Theory · Mathematics 2026-03-06 Danilo Hiroshi Matsuoka , Hudson da Silva Torrent

Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…

Statistics Theory · Mathematics 2026-05-13 Xin Bing , Chao Wang

In this work, we investigate high-dimensional kernel ridge regression (KRR) on i.i.d. Gaussian data with anisotropic power-law covariance. This setting differs fundamentally from the classical source & capacity conditions for KRR, where…

Machine Learning · Statistics 2025-10-07 Arie Wortsman , Bruno Loureiro

We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to…

Statistics Theory · Mathematics 2016-07-11 Gilles Blanchard , Nicole Krämer

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…

Machine Learning · Computer Science 2023-10-04 Tin Sum Cheng , Aurelien Lucchi , Ivan Dokmanić , Anastasis Kratsios , David Belius

General predictive models do not provide a measure of confidence in predictions without Bayesian assumptions. A way to circumvent potential restrictions is to use conformal methods for constructing non-parametric confidence regions, that…

Machine Learning · Statistics 2016-09-21 Evgeny Burnaev , Ivan Nazarov

Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm…

Statistics Theory · Mathematics 2020-01-03 Rui Tuo , Yan Wang , C. F. Jeff Wu

Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…

Machine Learning · Computer Science 2024-10-03 Mauro Bisiacco , Gianluigi Pillonetto

We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as…

Methodology · Statistics 2010-08-13 Gilles Blanchard , Nicole Kraemer

Kernel balancing weights provide confidence intervals for average treatment effects, based on the idea of balancing covariates for the treated group and untreated group in feature space, often with ridge regularization. Previous works on…

Machine Learning · Statistics 2024-07-08 Rahul Singh

Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…

Machine Learning · Computer Science 2018-05-22 Haim Avron , Michael Kapralov , Cameron Musco , Christopher Musco , Ameya Velingker , Amir Zandieh

Gaussian process (GP) regression is a fundamental tool in Bayesian statistics. It is also known as kriging and is the Bayesian counterpart to the frequentist kernel ridge regression. Most of the theoretical work on GP regression has focused…

Statistics Theory · Mathematics 2023-10-27 Simon Barthelmé , Pierre-Olivier Amblard , Nicolas Tremblay , Konstantin Usevich

This paper deals with the speed of convergence of the learning curve in a Gaussian process regression framework. The learning curve describes the average generalization error of the Gaussian process used for the regression. More…

Statistics Theory · Mathematics 2013-01-14 Loic Le Gratiet , Josselin Garnier

We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…

Machine Learning · Statistics 2025-09-16 Leonardo V. Santoro , Victor M. Panaretos

A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…

Machine Learning · Statistics 2025-04-07 Jianyu Hu , Juan-Pablo Ortega , Daiying Yin

We develop a framework for function classes generated by parametric ridge kernels: one-dimensional kernels composed with affine projections and averaged over a parameter measure. The induced kernels are positive definite, and the resulting…

Functional Analysis · Mathematics 2025-08-26 James Tian