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2012
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Nearly optimal solutions for the chow parameters problem and low-weight approximation of halfspaces

7 years 8 months ago
Nearly optimal solutions for the chow parameters problem and low-weight approximation of halfspaces
The Chow parameters of a Boolean function f : {−1, 1}n → {−1, 1} are its n + 1 degree-0 and degree-1 Fourier coefficients. It has been known since 1961 [Cho61, Tan61] that the (exact values of the) Chow parameters of any linear threshold function f uniquely specify f within the space of all Boolean functions, but until recently [OS11] nothing was known about efficient algorithms for reconstructing f (exactly or approximately) from exact or approximate values of its Chow parameters. We refer to this reconstruction problem as the Chow Parameters Problem. Our main result is a new algorithm for the Chow Parameters Problem which, given (sufficiently accurate approximations to) the Chow parameters of any linear threshold function f, runs in time ˜O(n2 )· (1/ǫ)O(log2 (1/ǫ)) and with high probability outputs a representation of an LTF f′ that is ǫ-close to f. The only previous algorithm [OS11] had running time poly(n) · 22 ˜O(1/ǫ2) . As a byproductof our approach, we show t...
Anindya De, Ilias Diakonikolas, Vitaly Feldman, Ro
Added 28 Sep 2012
Updated 28 Sep 2012
Type Journal
Year 2012
Where STOC
Authors Anindya De, Ilias Diakonikolas, Vitaly Feldman, Rocco A. Servedio
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