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非稀疏高维线性回归的典范阈值估计AI 解读

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix of the data. We propose a new family of estimators, called the canonical thresholding estimators, which pick largest regression coefficients in the canonical form. The estimators admit an explicit form and can be linked to LASSO and…

协方差矩阵特征子空间的假设检验AI 解读

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…