Related papers: Variable selection for the prediction of C[0,1]-va…

For a certain scaling of the initialization of stochastic gradient descent (SGD), wide neural networks (NN) have been shown to be well approximated by reproducing kernel Hilbert space (RKHS) methods. Recent empirical work showed that, for…

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…

We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors.…

Estimation of the mean and covariance functions is a fundamental problem in functional data analysis, particularly for discretely observed functional data. In this work, we study a regularization-based framework for estimating the mean and…

This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…

The main ideas behind the classical multivariate logistic regression model make sense when translated to the functional setting, where the explanatory variable $X$ is a function and the response $Y$ is binary. However, some important…

Estimating Kullback Leibler (KL) divergence from samples of two distributions is essential in many machine learning problems. Variational methods using neural network discriminator have been proposed to achieve this task in a scalable…

Sample reweighting is one of the most widely used methods for correcting the error of least squares learning algorithms in reproducing kernel Hilbert spaces (RKHS), that is caused by future data distributions that are different from the…

Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. Chakraborty et al. (2012) did a full hierarchical Bayesian analysis of nonlinear regression in such…

As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…

Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo…

This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

This paper reviews the main estimation and prediction results derived in the context of functional time series, when Hilbert and Banach spaces are considered, specially, in the context of autoregressive processes of order one (ARH(1) and…

Model-free time-to-event regression under confounding presents challenges due to biases introduced by causal and censoring sampling mechanisms. This phenomenology poses problems for classical non-parametric estimators like Beran's or the…

In this paper, an adaptive non-parametric method is proposed to estimate the scalar-valued nonlinear function that appears in uncertain systems governed by ordinary differential equations (ODEs). By employing an infinite-dimensional…

We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number…

Conformal prediction provides distribution-free prediction sets with finite-sample conditional guarantees. We build upon the RKHS-based framework of Gibbs et al. (2023), which leverages families of covariate shifts to provide approximate…

This paper builds on the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville…

The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…