Related papers: An RKHS model for variable selection in functional…

It is known that the membership in a given reproducing kernel Hilbert space (RKHS) of the samples of a Gaussian process $X$ is controlled by a certain nuclear dominance condition. However, it is less clear how to identify a "small" set of…

Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey…

We consider a spatial functional linear regression, where a scalar response is related to a square integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample…

In this paper, we develop a generalized theory of convolutional signal processing and neural networks for Reproducing Kernel Hilbert Spaces (RKHS). Leveraging the theory of algebraic signal processing (ASP), we show that any RKHS allows the…

Motivated by the need of processing functional-valued data, or more general, operatorvalued data, we introduce the notion of the operator reproducing kernel Hilbert space (ORKHS). This space admits a unique operator reproducing kernel which…

Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…

We consider policy evaluation in infinite-horizon discounted Markov decision problems (MDPs) with infinite spaces. We reformulate this task a compositional stochastic program with a function-valued decision variable that belongs to a…

This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…

We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and…

This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are…

Variable selection is considered in the setting of supervised binary classification with functional data $\{X(t),\ t\in[0,1]\}$. By "variable selection" we mean any dimension-reduction method which leads to replace the whole trajectory…

Consider the problem: given the data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network model and run gradient flow on the weights over time until…

This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel…

In this work, we develop and study an empirical projection operator scheme for solving nonparametric regression problems. This scheme is based on an approximate projection of the regression function over a suitable reproducing kernel…

This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…

The aim of this paper is to model an ordinal response variable in terms of vector-valued functional data included on a vector-valued RKHS. In particular, we focus on the vector-valued RKHS obtained when a geometrical object (body) is…

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…

We develop a comprehensive framework for spatio-temporal prediction of time-varying vector fields using operator-valued reproducing kernel Hilbert spaces (OV RKHS). By integrating Sobolev regularity with Koopman operator theory, we…

We study dynamic regret in online convex optimization, where the objective is to achieve low cumulative loss relative to an arbitrary benchmark sequence. By observing that competing with an arbitrary sequence of comparators…

Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local…