DIAMETERS OF SOME FINITE-DIMENSIONAL SETS AND CLASSES OF SMOOTH FUNCTIONS

By Udc, B. S. Kašin. 1977

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Citations in the corpus

The Power of Linear Reconstruction Attacks (2012, background): “The remaining6 boolean functions of two variables are degenerate.”
The LASSO Risk for Gaussian Matrices (2010, methodology): “(F.10) (d) For all 0 ≤ r, s ≤ t, and for any Lipschitz function ϕ : R2 → R , the following equations hold and all limits exist, are bounded and have degenerate distribution (i.e. they are constant random variables): lim N→∞ 〈hr+1, ϕ(hs+1, x0)〉 a.s.= lim N→∞ 〈hr+1, hs+1〉〈ϕ′(hs+1, x0)〉, (F.11) lim n→∞”
Compressive Sensing with structured random matrices (2012, methodology): “While the use of random matrices in sparse signal processing was rather uncommon before the advent of compressive sensing, we note that they were used quite successfully already much earlier, for instance in the very related problem from Banach space geometry of estimating Gelfand widths of `1 -ball”
Uncertainty Principle for Communication Compression in Distributed and Federated Learning and the Search for an Optimal Compressor (2020, unknown): “In an attempt to take a ﬁrst step in this direction, we design a new unbiased compression operator inspired by Kashin representation of vectors (Kashin, 1977), which we call Kashin Compression (KC).”
Convergence of Edge Computing and Deep Learning: A Comprehensive Survey (2019, unknown): “Kashin’s representation [206] can be utilized before subsampling as a basis transform to mitigate the error incurred by subsequent compression operations.”