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网络模型与谱降维方法中 varimax 旋转的渐近性质AI 解读

Abstract Varimax factor rotations, while popular among practitioners in psychology and statistics since being introduced by Kaiser (1958), have historically been viewed with skepticism and suspicion by some theoreticians and mathematical statisticians. Now, work by Rohe & Zeng (2023) provides new, fundamental insight: varimax rotations provably perform statistical estimation in certain classes of latent variable models when paired with spectral-based matrix truncations for…

信号加噪声矩阵模型：特征向量的偏差与波动AI 解读

Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science and applied mathematics. In this paper we characterize the behaviour of perturbed eigenvectors for a range of signal-plus-noise matrix models encountered in statistical and random-matrix-theoretic settings. We establish both first-order approximation results, i.e., sharp deviations, and second-order distributional limit theory, i.e.,…