论文标题
进入的恢复保证稀疏PCA通过稀疏算法保证
Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms
论文作者
论文摘要
稀疏主成分分析（PCA）是多个应用统计子场的普遍工具。虽然几个结果表征了主要特征向量的恢复误差，但这些结果通常在光谱或弗罗贝尼乌斯规范中。在本文中，我们在一般的高维副高斯设计下提供了入口处$ \ ell_ {2，\ infty} $界限。特别是，我们的结果适用于任何以高概率选择正确支持的算法，即那些稀疏的算法。我们的界限通过提供估计误差的表征更精细，而我们的证明使用最近为进入式子空间扰动理论开发的技术来改善已知结果。
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.
