Related papers: Towards Optimal Sobolev Norm Rates for the Vector-…
Learning rates for least-squares regression are typically expressed in terms of $L_2$-norms. In this paper we extend these rates to norms stronger than the $L_2$-norm without requiring the regression function to be contained in the…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
An asymptotic theory is established for linear functionals of the predictive function given by kernel ridge regression, when the reproducing kernel Hilbert space is equivalent to a Sobolev space. The theory covers a wide variety of linear…
We study theoretical properties of a broad class of regularized algorithms with vector-valued output. These spectral algorithms include kernel ridge regression, kernel principal component regression, various implementations of gradient…
We study kernel least-squares estimation under a norm constraint. This form of regularisation is known as Ivanov regularisation and it provides better control of the norm of the estimator than the well-established Tikhonov regularisation.…
In the misspecified kernel ridge regression problem, researchers usually assume the underground true function $f_{\rho}^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$…
Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…
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…
This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly…
Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…
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…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect…
We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a…
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…
Learning mappings between infinite-dimensional function spaces has achieved empirical success in many disciplines of machine learning, including generative modeling, functional data analysis, causal inference, and multi-agent reinforcement…
We address the consistency of a kernel ridge regression estimate of the conditional mean embedding (CME), which is an embedding of the conditional distribution of $Y$ given $X$ into a target reproducing kernel Hilbert space $\mathcal{H}_Y$.…
Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the sample size $n \asymp d^{\gamma}$ for some $\gamma > 0$.…
We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear…