The Gaussian Surface Area and Noise Sensitivity of Degree-d Polynomial Threshold Functions

Abstract. 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. Keywords. Gaussian Noise, Polynomial Threshold Functions, Machine Learning Subject classification. 68T05, 60E10

• Type: Conference
• Year: 2010
• Where: COCO
• Authors: Daniel M. Kane
• Keywords: Algorithms, COCO 2010, Gaussian Noise, Optimal Bounds, Polynomial Threshold Functions