Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms
Joshua Agterberg, Jeremias Sulam

TL;DR
This paper establishes entrywise error bounds for Sparse PCA under high-dimensional subgaussian models, providing a more detailed understanding of estimation accuracy for sparsistent algorithms.
Contribution
It introduces entrywise $ ext{ell}_{2, ext{infty}}$ bounds for Sparse PCA, improving upon existing spectral norm results and applicable to any sparsistent algorithm.
Findings
Provides entrywise $ ext{ell}_{2, ext{infty}}$ bounds for Sparse PCA
Results hold for any support-recovering sparsistent algorithms
Uses entrywise subspace perturbation techniques
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 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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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Blind Source Separation Techniques · Image and Signal Denoising Methods
MethodsPrincipal Components Analysis
