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NP-Hardness and Inapproximability of Sparse PCA

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arxiv 1502.05675 v2 pith:ZXHVOWKM submitted 2015-02-19 cs.LG cs.CCcs.DSmath.COstat.ML

classification cs.LGcs.CCcs.DSmath.COstat.ML
keywords sparseexcludereductionalgorithmsapproximationassumptionscliquecomplexity
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We give a reduction from {\sc clique} to establish that sparse PCA is NP-hard. The reduction has a gap which we use to exclude an FPTAS for sparse PCA (unless P=NP). Under weaker complexity assumptions, we also exclude polynomial constant-factor approximation algorithms.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Combinatorial Sparse PCA Beyond the Spiked Identity Model

    stat.ML 2026-03 accept novelty 8.0 of 10

    A restarted, oversampled, sample-split truncated power method provably recovers the sparse top eigenvector of any covariance with an eigengap using near-optimal samples.

  2. Detecting high-dimensional entanglement with simple measurements

    quant-ph 2026-08 conditional novelty 7.0 of 10

    A witness method detects high-dimensional Schmidt numbers using only strings of single-qubit Pauli measurements, demonstrated up to 16-dimensional photonic entanglement.

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