In this paper we discuss the problem of fitting `1 regularized prediction models in infinite (possibly non-countable) dimensional feature spaces. Our main contributions are: a. Deriving a generalization of `1 regularization based on measures which can be applied in non-countable feature spaces; b. Proving that the sparsity property of `1 regularization is maintained in infinite dimensions; c. D...

A new package crs is introduced for computing nonparametric regression (and quantile) splines in the presence of both continuous and categorical predictors. B-splines are employed in the regression model for the continuous predictors and kernel weighting is employed for the categorical predictors. We also develop a simple R interface to NOMAD, which is a mixed integer optimization solver used t...

The regularized long wave equation (RLW) is solved numerically by using the quintic B-spline Galerkin finite element method. The same method is applied to the time-split RLW equation. Comparison is made with both analytical solutions and some previous results. Propagation of solitary waves, interaction of two solitons are studied. © 2005 Elsevier B.V. All rights reserved. MSC: 65N30; 65D07; 76B25

This paper considers the problem of three dimensional surface reconstruction of non polyhedral objects through series of images taken from a moving camera. We propose a direct method of surface reconstruction which is based on regularized uniform bicubic B-spline surface patches 35]. This reconstruction is achieved by observing the motion of occluding contours 1, 9, 33], i.e., where the view li...

I discuss a theory of non-solar cosmic rays (CRs) based on a single type of CR source at all energies. All observed properties of CRs are predicted in terms of very simple and completely ‘standard’ physics. The source of CRs is extremely ‘economical’: it has only one parameter to be fitted to the enormous ensemble of all of the data. All other inputs are ‘priors’, that is theoretical or observa...

The stable spline (SS) kernel and the diagonal correlated (DC) kernel are two kernels that have been applied and studied extensively for kernel-based regularized LTI system identification. In this note, we show that similar to the derivation of the SS kernel, the continuous-time DC kernel can be derived by applying the same “stable” coordinate change to a “generalized” first-order spline kernel...

We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal, curvature-constrained snake is a cubic spline, irrespective of the form of the external energy field. Unfortunately, such regularized snakes suffer from slow co...

The treatment of chronic rhinosinusitis (CRS) requires an increasing use of medical and economic resources. Therefore, the assessment of objective and subjective outcome of different treatment strategies is of considerable interest. Validated quality of life (QOL) instruments are one important means to assess subjective outcome of the patients. Frequently used generic instruments are the Short ...

Inspired by ideas taken from the machine learning literature, new regularization techniques have been recently introduced in linear system identification. In particular, all the adopted estimators solve a regularized least squares problem, differing in the nature of the penalty term assigned to the impulse response. Popular choices include atomic and nuclear norms (applied to Hankel matrices) a...