The sharp MSE bound for the ℓ1-minimum-norm interpolator under isotropic Gaussian covariates is recovered via the geometry of symmetric Gaussian polytopes, without the convex Gaussian min-max theorem.
The Kannan-Lov\'asz-Simonovits Conjecture
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abstract
The Kannan-Lov\'asz-Simonovits conjecture says that the Cheeger constant of any logconcave density is achieved to within a universal, dimension-independent constant factor by a hyperplane-induced subset. Here we survey the origin and consequences of the conjecture (in geometry, probability, information theory and algorithms) as well as recent progress resulting in the current best bounds. The conjecture has lead to several techniques of general interest.
representative citing papers
Simplified proof of Klartag's CLT for convex bodies via log-concave functions, with appendix on thin shell implying CLT.
citing papers explorer
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Minimum Norm Interpolation via The Local Theory of Banach Spaces: The Role of Gaussianity
The sharp MSE bound for the ℓ1-minimum-norm interpolator under isotropic Gaussian covariates is recovered via the geometry of symmetric Gaussian polytopes, without the convex Gaussian min-max theorem.
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A simplified proof of CLT for convex bodies
Simplified proof of Klartag's CLT for convex bodies via log-concave functions, with appendix on thin shell implying CLT.