Related papers: Optimal Penalized Function-on-Function Regression …

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…

We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being…

In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…

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…

We consider the problem of constructing a regression model with a functional predictor and a functional response. We extend the functional linear model to the quadratic model, where the quadratic term also takes the interaction between the…

We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…

We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…

This paper considers the partially functional linear model (PFLM) where all predictive features consist of a functional covariate and a high dimensional scalar vector. Over an infinite dimensional reproducing kernel Hilbert space, the…

The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a…

This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression under the framework of learning theory. The algorithm…

Penalization procedures often suffer from their dependence on multiplying factors, whose optimal values are either unknown or hard to estimate from the data. We propose a completely data-driven calibration algorithm for this parameter in…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology…

In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence…

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 scalar-on-function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the…

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…

In this work we propose a generalized additive functional regression model for partially observed functional data. Our approach accommodates functional predictors of varying dimensions without requiring imputation of missing observations.…

In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular…