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

Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms