Related papers: General P-Splines for Non-Uniform B-Splines

We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty…

A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…

We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish…

In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the…

Detecting slender, overlapping structures remains a challenge in computational microscopy. While recent coordinate-based approaches improve detection, they often produce less accurate splines than pixel-based methods. We introduce a…

Physics-informed machine learning offers a promising framework for solving complex partial differential equations (PDEs) by integrating observational data with governing physical laws. However, learning PDEs with varying parameters and…

We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions,…

In this paper we develop flexible Krylov methods for efficiently computing regularized solutions to large-scale linear inverse problems with an $\ell_2$ fit-to-data term and an $\ell_p$ penalization term, for $p\geq 1$. First we approximate…

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…

Quantile regression has received increased attention in the statistics community in recent years. This article adapts an auxiliary variable method, commonly used in Bayesian variable selection for mean regression models, to the fitting of…

We study a new simple quadrature rule based on integrating a $C^1$ quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions…

The identification of predictive biomarkers from a large scale of covariates for subgroup analysis has attracted fundamental attention in medical research. In this article, we propose a generalized penalized regression method with a novel…

The marriage of recurrent neural networks and neural ordinary differential networks (ODE-RNN) is effective in modeling irregularly-observed sequences. While ODE produces the smooth hidden states between observation intervals, the RNN will…

In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…

In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the…

Generalized Linear Bandits (GLBs) are powerful extensions to the Linear Bandit (LB) setting, broadening the benefits of reward parametrization beyond linearity. In this paper we study GLBs in non-stationary environments, characterized by a…

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…

We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when…

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…

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a…