Polynomial Regression under Arbitrary Product Distributions

In recent work, Kalai, Klivans, Mansour, and Servedio [KKMS05] studied a variant of the "Low-Degree (Fourier) Algorithm" for learning under the uniform probability distribution on {0, 1}n . They showed that the L1 polynomial regression algorithm yields agnostic (tolerant to arbitrary noise) learning algorithms with respect to the class of threshold functions -- under certain restricted instance distributions, including uniform on {0, 1}n and Gaussian on Rn . In this work we show how all learning results based on the Low-Degree Algorithm can be generalized to give almost identical agnostic guarantees under arbitrary product distributions on instance spaces X1 ׷

• Type: Conference
• Year: 2008
• Where: COLT
• Authors: Eric Blais, Ryan O'Donnell, Karl Wimmer
• Keywords: Arbitrary Product, Arbitrary Product Spaces, COLT 2008, Machine Learning, Threshold Functions