Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm

02/23/2017
by   Simon Fischer, et al.
0

Learning rates for regularized least-squares algorithms are in most cases expressed with respect to the excess risk, or equivalently, the L_2-norm. For some applications, however, guarantees with respect to stronger norms such as the L_∞-norm, are desirable. We address this problem by establishing learning rates for a continuous scale of norms between the L_2- and the RKHS norm. As a byproduct we derive L_∞-norm learning rates, and in the case of Sobolev RKHSs we actually obtain Sobolev norm learning rates, which may also imply L_∞-norm rates for some derivatives. In all cases, we do not need to assume the target function to be contained in the used RKHS. Finally, we show that in many cases the derived rates are minimax optimal.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/12/2018

Optimal Rates of Sketched-regularized Algorithms for Least-Squares Regression over Hilbert Spaces

We investigate regularized algorithms combining with projection for leas...
research
01/17/2022

On Well-posedness and Minimax Optimal Rates of Nonparametric Q-function Estimation in Off-policy Evaluation

We study the off-policy evaluation (OPE) problem in an infinite-horizon ...
research
05/17/2018

Minimax regularization

Classical approach to regularization is to design norms enhancing smooth...
research
06/07/2023

From dense to sparse design: Optimal rates under the supremum norm for estimating the mean function in functional data analysis

In the setting of functional data analysis, we derive optimal rates of c...
research
02/08/2019

Beyond Least-Squares: Fast Rates for Regularized Empirical Risk Minimization through Self-Concordance

We consider learning methods based on the regularization of a convex emp...
research
04/11/2022

Local convergence rates of the least squares estimator with applications to transfer learning

Convergence properties of empirical risk minimizers can be conveniently ...
research
03/06/2019

A Priori Estimates of the Population Risk for Residual Networks

Optimal a priori estimates are derived for the population risk of a regu...

Please sign up or login with your details

Forgot password? Click here to reset