Concentration and moment inequalities for polynomials of independent random variables
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Hardness results for agnostically learning low-degree polynomial threshold functions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We prove asymptotically optimal bounds on the Gaussian noise sensitivity of degree-d polynomial threshold functions. These bounds translate into optimal bounds on the Gaussian surface area of such functions, and therefore imply new bounds on the running time of agnostic learning algorithms.