First poly-time 2 to q norm approximation algorithms beating the d^{1/4} baseline by polynomial factors (d^{1/8} for q=4) plus SOS certificates enabling improved robust mean/covariance estimation and clustering under q-moment bounds.
Hypercontractivity and its applications
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abstract
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of hypercontractivity, and also present some relatively recent applications of these techniques in computer science.
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cs.DS 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications
First poly-time 2 to q norm approximation algorithms beating the d^{1/4} baseline by polynomial factors (d^{1/8} for q=4) plus SOS certificates enabling improved robust mean/covariance estimation and clustering under q-moment bounds.