The (cubic) smoothing spline, of Schoenberg [S64] and Reinsch [R67], [R71], has become the most commonly used spline, particularly after the introduction of generalized cross validation by Craven and Wahba [CW79] for an automatic choice of the smoothing parameter. It is the purpose of this note to derive the computational details, in terms of B-splines, for the construction of the weighted smoo...

In the context of the derivative-free optimization of a smooth objective function, it has been shown that the worst case complexity of direct-search methods is of the same order as the one of steepest descent for derivative-based optimization, more precisely that the number of iterations needed to reduce the norm of the gradient of the objective function below a certain threshold is proportiona...

For spline smoothing one can rewrite the smooth estimation as a linear mixed model (LMM) where the smoothing parameter appears as the variance of spline basis coefficients. Smoothing methods that use basis functions with penalization can utilize maximum likelihood (ML) theory in LMM framework ([8]). We introduce the minimum description length (MDL) model selection criterion in LMM and propose a...

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector i...

This paper presents experiments with tracking time{varying parameters of a dynamic system applied to parameter estimation and smoothing of piecewise continuous function. The smoothing algorithm is based on bayesian computation of the probability distribution over the set of alternative hypotheses describing a set of alternative models of expected (possible) parameter development. The sequence o...

Abstract We compute the distribution of likelihoods from non-parametric iterative smoothing method over a set mock Pantheon-like type Ia supernova datasets. use this likelihood to test whether typical dark energy models are consistent with data and perform parameter estimation. In approach, consistency model is determined without need for comparison another alternative model. Simulating future ...

In this paper, we propose a spectral difference approach for noise power estimation in speech enhancement. The noise power estimate is given by recursively averaging past spectral power values using a smoothing parameter based on the current observation. The smoothing parameter in time and frequency is adjusted by the spectral difference between consecutive frames that can efficiently character...