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» A Small PRG for Polynomial Threshold Functions of Gaussians
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COCO
2010
Springer
149views Algorithms» more  COCO 2010»
13 years 7 months ago
The Gaussian Surface Area and Noise Sensitivity of Degree-d Polynomial Threshold Functions
Abstract. We prove asymptotically optimal bounds on the Gaussian noise sensitivity of degree-d polynomial threshold functions. These bounds translate into optimal bounds on the Gau...
Daniel M. Kane
STOC
2009
ACM
119views Algorithms» more  STOC 2009»
14 years 5 months ago
Explicit construction of a small epsilon-net for linear threshold functions
We give explicit constructions of epsilon nets for linear threshold functions on the binary cube and on the unit sphere. The size of the constructed nets is polynomial in the dime...
Yuval Rabani, Amir Shpilka
COCO
2010
Springer
144views Algorithms» more  COCO 2010»
13 years 8 months ago
A Regularity Lemma, and Low-Weight Approximators, for Low-Degree Polynomial Threshold Functions
We give a “regularity lemma” for degree-d polynomial threshold functions (PTFs) over the Boolean cube {−1, 1}n . Roughly speaking, this result shows that every degree-d PTF ...
Ilias Diakonikolas, Rocco A. Servedio, Li-Yang Tan...