Error Bounds for Piecewise Smooth and Switching Regression

Error Bounds for Piecewise Smooth and Switching Regression

The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a partition of the input space, while switching regression considers arbitrary switching laws. The paper derives generalization error bounds in these two settings...

Global error bounds for piecewise convex polynomials

In this paper, by examining the recession properties of convex polynomials, we provide a necessary and sufficient condition for a piecewise convex polynomial to have a Hölder-type global error bound with an explicit Hölder exponent. Our result extends the corresponding results of [25] from piecewise convex quadratic functions to piecewise convex polynomials.

Error bounds for bivariate piecewise hermite interpolation

Algorithms and Error Bounds for Multivariate Piecewise Constant Approximation

Let Ω be a bounded domain in R, d ≥ 2. Suppose that ∆ is a partition of Ω into a finite number of subsets ω ⊂ Ω called cells, where the default assumptions are just these: |ω| := meas(ω) > 0 for all ω ∈ ∆, |ω ∩ ω′| = 0 if ω 6= ω, and ∑ ω∈∆ |ω| = |Ω|. For a finite set D we denote its cardinality by |D|, so that |∆| stands for the number of cells ω in ∆. Given a function f : Ω → R, we are interes...

Nonparametric estimation of piecewise smooth regression functions

Estimation of univariate regression functions from bounded i.i.d. data is considered. Estimates are deened by minimizing a complexity penalized residual sum of squares over all piecewise polynomials. The integrated squared error of these estimates achieves for piecewise p-smooth regression functions the rate (ln 2 (n)=n) 2p 2p+1 .