SoS Certifiability of Subgaussian Distributions and Its Algorithmic Applications
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3717823.3718183.pdf
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Author(s)
Diakonikolas, Ilias
Hopkins, Samuel
Pensia, Ankit
Tiegel, Stefan
Date Issued
June 15, 2025
Publisher
ACM|Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Citation
Ilias Diakonikolas, Samuel B. Hopkins, Ankit Pensia, and Stefan Tiegel. 2025. SoS Certifiability of Subgaussian Distributions and Its Algorithmic Applications. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC '25). Association for Computing Machinery, New York, NY, USA, 1689–1700.
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Final published version
Abstract
We prove that there is a universal constant C>0 so that for every d ∈ ℕ, every centered subgaussian distribution D on ℝd, and every even p ∈ ℕ, the d-variate polynomial (Cp)p/2 · ||v||2p − EX ∼ D ⟨ v,X⟩p is a sum of square polynomials. This establishes that every subgaussian distribution is SoS-certifiably subgaussian—a condition that yields efficient learning algorithms for a wide variety of high-dimensional statistical tasks. As a direct corollary, we obtain computationally efficient algorithms with near-optimal guarantees for the following tasks, when given samples from an arbitrary subgaussian distribution: robust mean estimation, list-decodable mean estimation, clustering mean-separated mixture models, robust covariance-aware mean estimation, robust covariance estimation, and robust linear regression. Our proof makes essential use of Talagrand’s generic chaining/majorizing measures theorem.
Description
STOC ’25, Prague, Czechia
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3717823.3718183
