Do semidefinite relaxations solve sparse PCA up to the information limit?
半正定松弛能否将稀疏主成分分析推进至信息极限？
Estimating the leading principal components of data, assuming they are sparse, is a central task in modern high-dimensional statistics. Many algorithms were developed for this sparse PCA problem, from simple diagonal thresholding to sophisticated semidefinite programming (SDP) methods. A key theoretical question is under what conditions can such algorithms recover the sparse principal components? We study this question for a single-spike model with an $\ell_{0}$-sparse…