Lévy Adaptive B-spline Regression via Overcomplete Systems

by   Sewon Park, et al.

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 (Lévy Adaptive B-Spline regression) model, an extension of the LARK models, for the estimation of functions with varying degrees of smoothness. LABS model is a LARK with B-spline bases as generating kernels. The B-spline basis consists of piecewise k degree polynomials with k-1 continuous derivatives and can express systematically functions with varying degrees of smoothness. By changing the orders of the B-spline basis, LABS can systematically adapt the smoothness of functions, i.e., jump discontinuities, sharp peaks, etc. Results of simulation studies and real data examples support that this model catches not only smooth areas but also jumps and sharp peaks of functions. The proposed model also has the best performance in almost all examples. Finally, we provide theoretical results that the mean function for the LABS model belongs to the certain Besov spaces based on the orders of the B-spline basis and that the prior of the model has the full support on the Besov spaces.



There are no comments yet.


page 1

page 2

page 3

page 4


Multivariate Lévy Adaptive B-Spline Regression

We develop a fully Bayesian nonparametric regression model based on a Lé...

Multidimensional Adaptive Penalised Splines with Application to Neurons' Activity Studies

P-spline models have achieved great popularity both in statistical and i...

Efficient Estimation of Pathwise Differentiable Target Parameters with the Undersmoothed Highly Adaptive Lasso

We consider estimation of a functional parameter of a realistically mode...

Smoothly varying ridge regularization

A basis expansion with regularization methods is much appealing to the f...

B-spline-like bases for C^2 cubics on the Powell-Sabin 12-split

For spaces of constant, linear, and quadratic splines of maximal smoothn...

Extension Operators for Trimmed Spline Spaces

We develop a discrete extension operator for trimmed spline spaces consi...

Shortest Multi-Spline Bases for Generalized Sampling

Generalized sampling consists in the recovery of a function f, from the ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.