Related papers: An RKHS model for variable selection in functional…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…
We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…
Functional linear and single-index models are core regression methods in functional data analysis and are widely used for performing regression in a wide range of applications when the covariates are random functions coupled with scalar…
This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear…
In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the…
In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…
This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null…
Motivated by the inherent heterogeneity observed in many functional or imaging datasets, this paper focuses on subgroup learning in functional or image responses. While change-plane analysis has demonstrated empirical success in practice,…
Variable selection is essential in high-dimensional data analysis. Although various variable selection methods have been developed, most rely on the linear model assumption. This article proposes a nonparametric variable selection method…
A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…
Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…
In this paper, we introduce a new distribution regression model for probability distributions. This model is based on a Reproducing Kernel Hilbert Space (RKHS) regression framework, where universal kernels are built using Wasserstein…
Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed…
Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…
We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-invariant systems, this class covers nonlinear systems modeled…
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…