Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Average sensitivity and noise sensitivity of polynomial threshold
  functions   We give the first non-trivial upper bounds on the average sensitivity and
noise sensitivity of degree-$d$ polynomial threshold functions (PTFs). These
bounds hold both for PTFs over the Boolean hypercube and for PTFs over $\R^n$
under the standard $n$-dimensional Gaussian distribution. Our bound on the
Boolean average sensitivity of PTFs represents progress towards the resolution
of a conjecture of Gotsman and Linial \cite{GL:94}, which states that the
symmetric function slicing the middle $d$ layers of the Boolean hypercube has
the highest average sensitivity of all degree-$d$ PTFs. Via the $L_1$
polynomial regression algorithm of Kalai et al. \cite{KKMS:08}, our bounds on
Gaussian and Boolean noise sensitivity yield polynomial-time agnostic learning
algorithms for the broad class of constant-degree PTFs under these input
distributions.
  The main ingredients used to obtain our bounds on both average and noise
sensitivity of PTFs in the Gaussian setting are tail bounds and
anti-concentration bounds on low-degree polynomials in Gaussian random
variables \cite{Janson:97,CW:01}. To obtain our bound on the Boolean average
sensitivity of PTFs, we generalize the ``critical-index'' machinery of
\cite{Servedio:07cc} (which in that work applies to halfspaces, i.e. degree-1
PTFs) to general PTFs. Together with the "invariance principle" of
\cite{MOO:05}, this lets us extend our techniques from the Gaussian setting to
the Boolean setting. Our bound on Boolean noise sensitivity is achieved via a
simple reduction from upper bounds on average sensitivity of Boolean PTFs to
corresponding bounds on noise sensitivity.

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The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol