Gaussian bounds for noise correlation of resilient functions
Name
1704.04745.pdf
Description
Submitted version
Size
271.63 KB
Format
Adobe PDF
Checksum (MD5)
0cf78301a3e25d1ebd1f8545a9ba4dcc
Author(s)
Mossel, Elchanan
Date Issued
2020
Journal
Israel Journal of Mathematics
Publisher
Springer Science and Business Media LLC
Version
Original manuscript
Abstract
© 2019, The Hebrew University of Jerusalem. Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp Gaussian bounds for the expected correlation of ℓ low influence functions f(1), …, f(ℓ):Ωn → [0, 1], where the inputs to the functions are correlated via the n-fold tensor of distribution P on Ωℓ in the following way: For each 1 ≤ i ≤ n, the vector consisting of the i’-th inputs to the ℓ functions is sampled according to P. It is natural to ask if the condition of low influences can be relaxed to the condition that the function has vanishing Fourier coefficients. Here and g we further show that if f, g have a noisy inner product that exceeds the Gaussian bound, then the Fourier supports of their large coefficients intersect.
MIT Department
Statistics and Data Science Center (Massachusetts Institute of Technology)
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/S11856-019-1951-X
