Sharp Theoretical Analysis for Nonparametric Testing Under Random Projection
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. As a by-product, the lower bound of projection dimension for minimax optimal estimation derived in Yang (2017) is proven to be sharp. One technical contribution is to establish upper bounds for a range of tail sums of empirical kernel eigenvalues.
Cite
Text
Liu et al. "Sharp Theoretical Analysis for Nonparametric Testing Under Random Projection." Conference on Learning Theory, 2019.Markdown
[Liu et al. "Sharp Theoretical Analysis for Nonparametric Testing Under Random Projection." Conference on Learning Theory, 2019.](https://mlanthology.org/colt/2019/liu2019colt-sharp/)BibTeX
@inproceedings{liu2019colt-sharp,
title = {{Sharp Theoretical Analysis for Nonparametric Testing Under Random Projection}},
author = {Liu, Meimei and Shang, Zuofeng and Cheng, Guang},
booktitle = {Conference on Learning Theory},
year = {2019},
pages = {2175-2209},
volume = {99},
url = {https://mlanthology.org/colt/2019/liu2019colt-sharp/}
}