Nonparametric Testing Under Randomized Sketching
Nonparametric Testing Under Randomized Sketching
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DOI：
10.1109/tpami.2021.3063223
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发表时间：
2021-03
影响因子：
23.6
通讯作者：
Meimei Liu;Zuofeng Shang;Yun Yang;Guang Cheng
中科院分区：
文献类型：
--
作者：
Meimei Liu;Zuofeng Shang;Yun Yang;Guang Cheng
非参数推理的一个共同挑战是当数据量很大时其高计算复杂度。在本文中，我们开发了计算效率的非参数检验采用随机投影策略。在特定的核岭回归设置中，提出了一种简单的基于距离的检验统计量。值得注意的是，我们推导出的最小数量的随机预测，这是足以实现测试的最优性方面的极大极小率。进一步建立了一种不需要规则性先验知识的自适应测试方法。一个技术上的贡献是建立一个范围内的经验核特征值的尾和的上界。仿真和真实的数据分析进行支持我们的理论。
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.