论文标题
样品协方差矩阵的定量确定性等效性具有一般依赖性结构
Quantitative deterministic equivalent of sample covariance matrices with a general dependence structure
论文作者
论文摘要
我们研究由I.I.D.矩形随机矩阵产生的样品协方差矩阵。列。以前知道，当光谱参数远离实际轴时，这些矩阵的分解是确定性的。我们通过证明涉及尺寸和频谱参数的定量界限来扩展这项工作，特别是使其更接近实际的正线。作为应用，我们获得了这些通用模型的经验光谱分布的Kolmogorov距离中收敛的新结合。我们还将我们的框架应用于机器学习中随机特征模型的正规化问题，而没有高斯假设。
We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away from the real axis. We extend this work by proving quantitative bounds involving both the dimensions and the spectral parameter, in particular allowing it to get closer to the real positive semi-line. As applications, we obtain a new bound for the convergence in Kolmogorov distance of the empirical spectral distributions of these general models. We also apply our framework to the problem of regularization of Random Features models in Machine Learning without Gaussian hypothesis.
