论文标题
协方差矩阵特征空间的假设检验
Hypothesis testing for eigenspaces of covariance matrix
论文作者
论文摘要
协方差矩阵的特征空间在统计机器学习中起着重要作用，在各种现代算法中产生。定量地，用光谱投影仪来描述特征空间很方便。这项工作着重于在单样本和两样本方案中对光谱投影仪的假设测试。我们基于开发的特定矩阵规范来提出新的测试，以利用光谱投影仪的结构。引入和分析了一种新的独立关注的重采样技术：它是众所周知的乘数引导程序的替代方法，可大大降低基于自举的方法的计算复杂性。我们为程序的I型错误提供了理论保证，这显着改善了先前获得的现场结果。此外，我们分析了测试的能力。与先前开发的方法相比，数值实验表明了所提出的方法的良好性能。
Eigenspaces of covariance matrices play an important role in statistical machine learning, arising in variety of modern algorithms. Quantitatively, it is convenient to describe the eigenspaces in terms of spectral projectors. This work focuses on hypothesis testing for the spectral projectors, both in one- and two-sample scenario. We present new tests, based on a specific matrix norm developed in order to utilize the structure of the spectral projectors. A new resampling technique of independent interest is introduced and analyzed: it serves as an alternative to the well-known multiplier bootstrap, significantly reducing computational complexity of bootstrap-based methods. We provide theoretical guarantees for the type-I error of our procedures, which remarkably improve the previously obtained results in the field. Moreover, we analyze power of our tests. Numerical experiments illustrate good performance of the proposed methods compared to previously developed ones.
