Related papers: A novel approach for estimating functions in the m…

We propose a novel approach to nonlinear functional regression, called the Mapping-to-Parameter function model, which addresses complex and nonlinear functional regression problems in parameter space by employing any supervised learning…

Motivated by recent work involving the analysis of leveraging spatial correlations in sparsified mean estimation, we present a novel procedure for constructing covariance estimator. The proposed Random-knots (Random-knots-Spatial) and…

In this paper, we present a nonlinear least-squares fitting algorithm using B-splines with free knots. Since its performance strongly depends on the initial estimation of the free parameters (i.e. the knots), we also propose a fast and…

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…

This paper presents a new approach to selecting knots at the same time as estimating the B-spline regression model. Such simultaneous selection of knots and model is not trivial, but our strategy can make it possible by employing a…

In this paper we introduce a new method for automatically selecting knots in spline regression. The approach consists in setting a large number of initial knots and fitting the spline regression through a penalized likelihood procedure…

In multivariate spline regression, the number and locations of knots influence the performance and interpretability significantly. However, due to non-differentiability and varying dimensions, there is no desirable frequentist method to…

Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface models, they…

We consider the problems of variable selection and estimation in nonparametric additive regression models for high-dimensional data. In recent years, several methods have been proposed to model nonlinear relationships when the number of…

Fitting B-splines to discrete data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently and robustly approximated with B-splines by…

The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant…

The estimation of functions with varying degrees of smoothness is a challenging problem in the nonparametric function estimation. In this paper, we propose the LABS (L\'{e}vy Adaptive B-Spline regression) model, an extension of the LARK…

Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…

We propose a new method for model selection and model fitting in multivariate nonparametric regression models, in the framework of smoothing spline ANOVA. The ``COSSO'' is a method of regularization with the penalty functional being the sum…

In this paper we propose a model selection approach to fit a regression model using splines with a variable number of knots. We introduce a penalized criterion to estimate the number and the position of the knots where to anchor the splines…

The fused lasso, also known as total-variation denoising, is a locally-adaptive function estimator over a regular grid of design points. In this paper, we extend the fused lasso to settings in which the points do not occur on a regular…

We develop a fully automatic Bayesian Lasso via variational inference. This is a scalable procedure for approximating the posterior distribution. Special attention is driven to the knot selection in regression spline. In order to carry…

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…

This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…

In this paper, we propose a novel adaptive-rank method for simulating multi-scale BGK equations, based on a greedy sampling strategy. The method adaptively selects important rows and columns of the solution matrix and updates them using a…