Related papers: General P-Splines for Non-Uniform B-Splines
We introduce a smooth B-spline discretization in polar coordinates on the unit disc that corrects the loss of regularity present at the origin caused by the coordinate singularity in standard tensor-product B-spline formulations. The method…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space…
P-splines provide a flexible and computationally efficient smoothing framework and are commonly used for derivative estimation in functional data. Including an additive penalty term in P-splines has been shown to improve estimates of…
Calibrating neural networks is of utmost importance when employing them in safety-critical applications where the downstream decision making depends on the predicted probabilities. Measuring calibration error amounts to comparing two…
The B-spline copula function is defined by a linear combination of elements of the normalized B-spline basis. We develop a modified EM algorithm, to maximize the penalized pseudo-likelihood function, wherein we use the smoothly clipped…
The paper proposes, an algorithm to produce novel m-point (for any integer m>=2) binary non-stationary subdivision scheme. It has been developed using uniform trigonometric B-spline basis functions and smoothness is being analyzed using the…
We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares…
This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding…
Given a graph $G$ whose edges are labeled by ideals of a commutative ring $R$ with identity, a generalized spline is a vertex labeling of $G$ by the elements of $R$ so that the difference of labels on adjacent vertices is an element of the…
In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the…
Regularized regression has become very popular nowadays, particularly on high-dimensional problems where the addition of a penalty term to the log-likelihood allows inference where traditional methods fail. A number of penalties have been…
We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent…
We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…
A fast algorithm for B-splines in mixed models is presented. B-splines have local support and are computational attractive, because the corresponding matrices are sparse. A key element of the new algorithm is that the local character of…
Local perturbations around contours strongly disturb the final result of computer vision tasks. It is common to introduce a priori information in the estimation process. Improvement can be achieved via a deformable model such as the snake…
In this paper I uncover and explain---using contour integrals and residues---a connection between cubic splines and a popular compact finite difference formula. The connection is that on a uniform mesh the simplest Pad\'e scheme for…
We consider the periodic dispersion generalized Benjamin-Ono equations with polynomial nonlinearity. We establish the nonlinear smoothing properties of these equations, according to which the difference between the solution and the linear…
A new representation of splines that targets efficiency in the analysis of functional data is implemented. The efficiency is achieved through two novel features: using the recently introduced orthonormal spline bases, the so-called {\it…
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…