Smoothed discrepancy principle as an early stopping rule in RKHS

Yaroslav Averyanov (1) , Alain A. Celisse (2, 1)

1 Inria Lille - Nord Europe
2 LPP - Laboratoire Paul Painlevé - UMR 8524

In this paper we work on the estimation of a regression function that belongs to a polynomial decay reproducing kernel Hilbert space (RKHS). We describe spectral filter framework for our estimator that allows us to deal with several iterative algorithms: gradient descent, Tikhonov regularization, etc. The main goal of the paper is to propose a new early stopping rule by introducing smoothing parameter for empirical risk of the estimator in order to improve the previous results [1] on discrepancy principle. Theoretical justifications as well as simulations experiments for the proposed rule are provided.

Mots clés: Non-parametric regression; Regularization; Kernels; Stopping rules; regularization; kernels; stopping rules

Domaines: Statistiques [stat]; Machine Learning [stat.ML]

Yaroslav Averyanov, Alain A. Celisse. Smoothed discrepancy principle as an early stopping rule in RKHS. 51es Journées de Statistique, Jun 2019, Nancy, France. ⟨hal-02427696v3⟩