New Results for Learning Noisy Parities and Halfspaces

We address well-studied problems concerning the learnability of parities and halfspaces in the presence of classification noise. Learning of parities under the uniform distribution with random classification noise, also called the noisy parity problem is a famous open problem in computational learning. We reduce a number of basic problems regarding learning under the uniform distribution to learning of noisy parities, thus highlighting the central role of this problem for learning under the uniform distribution. We show that under the uniform distribution, learning parities with adversarial classification noise reduces to learning parities with random classification noise. Together with the parity learning algorithm of Blum et al. [BKW03], this gives the first nontrivial algorithm for learning parities with adversarial noise. We show that learning of DNF expressions reduces to learning noisy parities of just logarithmic number of variables. We show that learning of k-juntas reduc...

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: Vitaly Feldman, Parikshit Gopalan, Subhash Khot, Ashok Kumar Ponnuswami
• Keywords: Classification Noise, FOCS 2006, Random Classification Noise, Theoretical Computer Science, Uniform Distribution