1 research outputs found
Boolean Functions with Biased Inputs: Approximation and Noise Sensitivity
This paper considers the problem of approximating a Boolean function
using another Boolean function from a specified class. Two classes of
approximating functions are considered: -juntas, and linear Boolean
functions. The input bits of the function are assumed to be independently
drawn from a distribution that may be biased. The quality of approximation is
measured by the mismatch probability between and the approximating function
. For each class, the optimal approximation and the associated mismatch
probability is characterized in terms of the biased Fourier expansion of .
The technique used to analyze the mismatch probability also yields an
expression for the noise sensitivity of in terms of the biased Fourier
coefficients, under a general i.i.d. input perturbation model.Comment: 5 pages, 2 figures, To appear in IEEE ISIT 201