Related papers: Variable Selection and Minimax Prediction in High-…
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…
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…
Under the reproducing kernel Hilbert spaces (RKHS), we consider the penalized least-squares of the partially functional linear models (PFLM), whose predictor contains both functional and traditional multivariate parts, and the multivariate…
This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel…
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…
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…
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.…
Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…
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…
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…
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…
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…
This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…
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…
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…
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…
Applications of functional data with large numbers of predictors have grown precipitously in recent years, driven, in part, by rapid advances in genotyping technologies. Given the large numbers of genetic mutations encountered in genetic…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under high-dimensional multivariate functional data setting.…
This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents…