Nonparametric Testing Under Randomized Sketching

Document Type

Article

Publication Date

8-1-2022

Abstract

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the specific kernel ridge regression setup, a simple distance-based test statistic is proposed. Notably, we derive the minimum number of random projections that is sufficient for achieving testing optimality in terms of the minimax rate. An adaptive testing procedure is further established without prior knowledge of regularity. One technical contribution is to establish upper bounds for a range of tail sums of empirical kernel eigenvalues. Simulations and real data analysis are conducted to support our theory.

Identifier

85102269934 (Scopus)

Publication Title

IEEE Transactions on Pattern Analysis and Machine Intelligence

External Full Text Location

https://doi.org/10.1109/TPAMI.2021.3063223

e-ISSN

19393539

ISSN

01628828

PubMed ID

33656986

First Page

4280

Last Page

4290

Issue

8

Volume

44

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