Related papers: Kernel-based estimation for partially functional l…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
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…
The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…
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…
We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
This paper proposes distributed estimation procedures for three scalar-on-function regression models: the functional linear model (FLM), the functional non-parametric model (FNPM), and the functional partial linear model (FPLM). The…
Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$…
Functional covariates are common in many medical, biodemographic, and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study…
We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…
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…
Function-on-function linear regression is important for understanding the relationship between the response and the predictor that are both functions. In this article, we propose a reproducing kernel Hilbert space approach to…
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…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
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…
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…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
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…
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…