Related papers: Streaming kernel regression with provably adaptive…

We propose a kernel regression method to predict a target signal lying over a graph when an input observation is given. The input and the output could be two different physical quantities. In particular, the input may not be a graph signal…

Regularization is an essential element of virtually all kernel methods for nonparametric regression problems. A critical factor in the effectiveness of a given kernel method is the type of regularization that is employed. This article…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…

We study recursive regularized learning algorithms in the reproducing kernel Hilbert space (RKHS) with non-stationary online data streams. We introduce the concept of random Tikhonov regularization path and decompose the tracking error of…

We study kernel-based estimation of nonparametric time-varying parameters (TVPs) in linear models. Our contributions are threefold. First, we establish consistency and asymptotic normality of the kernel-based estimator for a broad class of…

Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…

Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…

We study contextual bandits with finitely many actions in which the reward of each arm follows a single-index model with an arm-specific index parameter and an unknown nonparametric link function. We consider a regime in which arms…

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…

Sparse regression has been a popular approach to perform variable selection and enhance the prediction accuracy and interpretability of the resulting statistical model. Existing approaches focus on offline regularized regression, while the…

Polynomial kernel regression is one of the standard and state-of-the-art learning strategies. However, as is well known, the choices of the degree of polynomial kernel and the regularization parameter are still open in the realm of model…

Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…

Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…

We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework. The data set of size n is partitioned into $m=O(n^\alpha)$ disjoint subsets. On each subset, some…

Recent works have shown that on sufficiently over-parametrized neural nets, gradient descent with relatively large initialization optimizes a prediction function in the RKHS of the Neural Tangent Kernel (NTK). This analysis leads to global…

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…

Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality…