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Poster
Early Stopping for Nonparametric Testing
Meimei Liu · Guang Cheng

Wed Dec 05 07:45 AM -- 09:45 AM (PST) @ Room 517 AB #101
in Wed Poster Session A »

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. All obtained results hold for various kernel classes, including Sobolev smoothness classes and Gaussian kernel classes.

Keywords: Learning Theory · Regularization
[ Paper] 

Author Information

Meimei Liu (Duke University)
Guang Cheng (Purdue University)

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