Computational Equivalence of Spiked Covariance and Spiked Wigner Models via Gram-Schmidt Perturbation

Guy Bresler, Alina Harbuzova
Proceedings of Thirty Eighth Conference on Learning Theory, PMLR 291:594-595, 2025.

Abstract

In this work, we show the first average-case reduction transforming the sparse Spiked Covariance Model into the sparse Spiked Wigner Model and as a consequence obtain the first computational equivalence result between two well-studied high-dimensional statistics models. Our approach leverages a new perturbation equivariance property for Gram-Schmidt orthogonalization, enabling removal of dependence in the noise while preserving the signal.

Cite this Paper

BibTeX
@InProceedings{pmlr-v291-bresler25b, title = {Computational Equivalence of Spiked Covariance and Spiked Wigner Models via Gram-Schmidt Perturbation}, author = {Bresler, Guy and Harbuzova, Alina}, booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory}, pages = {594--595}, year = {2025}, editor = {Haghtalab, Nika and Moitra, Ankur}, volume = {291}, series = {Proceedings of Machine Learning Research}, month = {30 Jun--04 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v291/main/assets/bresler25b/bresler25b.pdf}, url = {https://proceedings.mlr.press/v291/bresler25b.html}, abstract = {In this work, we show the first average-case reduction transforming the sparse Spiked Covariance Model into the sparse Spiked Wigner Model and as a consequence obtain the first computational equivalence result between two well-studied high-dimensional statistics models. Our approach leverages a new perturbation equivariance property for Gram-Schmidt orthogonalization, enabling removal of dependence in the noise while preserving the signal.} }
Endnote
%0 Conference Paper %T Computational Equivalence of Spiked Covariance and Spiked Wigner Models via Gram-Schmidt Perturbation %A Guy Bresler %A Alina Harbuzova %B Proceedings of Thirty Eighth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2025 %E Nika Haghtalab %E Ankur Moitra %F pmlr-v291-bresler25b %I PMLR %P 594--595 %U https://proceedings.mlr.press/v291/bresler25b.html %V 291 %X In this work, we show the first average-case reduction transforming the sparse Spiked Covariance Model into the sparse Spiked Wigner Model and as a consequence obtain the first computational equivalence result between two well-studied high-dimensional statistics models. Our approach leverages a new perturbation equivariance property for Gram-Schmidt orthogonalization, enabling removal of dependence in the noise while preserving the signal.
APA
Bresler, G. & Harbuzova, A.. (2025). Computational Equivalence of Spiked Covariance and Spiked Wigner Models via Gram-Schmidt Perturbation. Proceedings of Thirty Eighth Conference on Learning Theory, in Proceedings of Machine Learning Research 291:594-595 Available from https://proceedings.mlr.press/v291/bresler25b.html.

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