Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms

2022/02/08 by Agterberg, Joshua, Sulam, Jeremias
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2202.04061

Abstract

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 ℓ_2,∞ 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.

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