Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral or Frobenius norms. In this paper, we provide entrywise $\ell_{2,\infty}$ bounds for Sparse PCA under a general high-dimensional subgaussian design. In particular, our results hold for any algorithm that selects the correct support with high probability, those that are sparsistent. Our bound improves upon known results by providing a finer characterization of the estimation error, and our proof uses techniques recently developed for entrywise subspace perturbation theory.

翻译：粗化主元件分析( PCA) 是众多应用统计数据子领域的常用工具。 虽然有几项结果是主要源生物的回收错误的特征, 但这些结果通常是在光谱或Frobenius 规范中。 在本文中, 我们根据普通高维亚双陆基设计为 Sparse 五氯苯甲醚提供输入值$\ =2,\ infty}$ 的界限。 特别是, 我们的结果表明, 任何选择概率高的正确支持的算法, 都具有任意性。 我们的界限通过对估计错误进行精细的描述来改进已知结果, 并且我们的证据使用最近开发的用于进化子空间渗透理论的技术 。