Related papers: Nonlinear Multivariate Function-on-function Regres…

We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the…

An extension of reproducing kernel Hilbert space (RKHS) theory provides a new framework for modeling functional regression models with functional responses. The approach only presumes a general nonlinear regression structure as opposed to…

In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…

A mathematical model for variable selection in functional regression models with scalar response is proposed. By "variable selection" we mean a procedure to replace the whole trajectories of the functional explanatory variables with their…

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…

Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…

This paper proposes a new nonlinear approach for additive functional regression with functional response based on kernel methods along with some slight reformulation and implementation of the linear regression and the spectral additive…

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

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…

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…

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…

Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…

High-dimensional functional data have become increasingly prevalent in modern applications such as high-frequency financial data and neuroimaging data analysis. We investigate a class of high-dimensional linear regression models, where each…

We propose a novel Bayesian methodology for inference in functional linear and logistic regression models based on the theory of reproducing kernel Hilbert spaces (RKHS's). We introduce general models that build upon the RKHS generated by…

We present a novel framework for variable selection in Fr\'echet regression with responses in general metric spaces, a setting increasingly relevant for analyzing non-Euclidean data such as probability distributions and covariance matrices.…

A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…

Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…

This paper presents new results on Functional Analysis of Variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is considered…

High-dimensional functional data are becoming increasingly common in fields such as environmental monitoring and neuroimaging. This paper studies high-dimensional functional linear regression models that relate a scalar response to…

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…