Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boolean Functions with Biased Inputs: Approximation and Noise
  Sensitivity   This paper considers the problem of approximating a Boolean function $f$
using another Boolean function from a specified class. Two classes of
approximating functions are considered: $k$-juntas, and linear Boolean
functions. The $n$ 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 $f$ and the approximating function
$g$. For each class, the optimal approximation and the associated mismatch
probability is characterized in terms of the biased Fourier expansion of $f$.
The technique used to analyze the mismatch probability also yields an
expression for the noise sensitivity of $f$ in terms of the biased Fourier
coefficients, under a general i.i.d. input perturbation model.

8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ