Early Stopping for Nonparametric Testing

Meimei Liu; Guang Cheng

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arXiv · 1805.09950

Early Stopping for Nonparametric Testing

Meimei Liu·Guang Cheng

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Abstract

Early stopping of iterative algorithms is an algorithmic regularization method to avoid over-fitting in estimation and classification. In this paper, we show that early stopping can also be applied to obtain the minimax optimal testing in a general non-parametric setup. Specifically, a Wald-type test statistic is obtained based on an iterated estimate produced by functional gradient descent algorithms in a reproducing kernel Hilbert space. A notable contribution is to establish a "sharp" stopping rule: when the number of iterations achieves an optimal order, testing optimality is achievable; otherwise, testing optimality becomes impossible. As a by-product, a similar sharpness result is also derived for minimax optimal estimation under early stopping studied in [11] and [19]. All obtained results hold for various kernel classes, including Sobolev smoothness classes and Gaussian kernel classes.

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Meimei Liu, Guang Cheng. 2018-05-25. Early Stopping for Nonparametric Testing. https://arxiv.org/abs/1805.09950

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