Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms

Joshua Agterberg, Jeremias Sulam
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:6591-6629, 2022.

Abstract

Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfield 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 bounds 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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v151-agterberg22a, title = { Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms }, author = {Agterberg, Joshua and Sulam, Jeremias}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {6591--6629}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/agterberg22a/agterberg22a.pdf}, url = {https://proceedings.mlr.press/v151/agterberg22a.html}, abstract = { Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfield 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 bounds 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. } }
Endnote
%0 Conference Paper %T Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms %A Joshua Agterberg %A Jeremias Sulam %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-agterberg22a %I PMLR %P 6591--6629 %U https://proceedings.mlr.press/v151/agterberg22a.html %V 151 %X Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfield 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 bounds 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.
APA
Agterberg, J. & Sulam, J.. (2022). Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:6591-6629 Available from https://proceedings.mlr.press/v151/agterberg22a.html.

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