2021/02/11 by Jie Shen, Shen, Jie · 1 citation
Computer Science · #Data Structures and Algorithms (cs.DS) #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Machine Learning and ELM
paper · pdf · doi:10.48550/arxiv.2102.06247
openalex publication_date 2021/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study efficient PAC learning of homogeneous halfspaces in ℝd in the presence of malicious noise of Valiant (1985). This is a challenging noise model and only until recently has near-optimal noise tolerance bound been established under the mild condition that the unlabeled data distribution is isotropic log-concave. However, it remains unsettled how to obtain the optimal sample complexity simultaneously. In this work, we present a new analysis for the algorithm of Awasthi et al. (2017) and show that it essentially achieves the near-optimal sample complexity bound of O(d), improving the best known result of O(d2). Our main ingredient is a novel incorporation of a matrix Chernoff-type inequality to bound the spectrum of an empirical covariance matrix for well-behaved distributions, in conjunction with a careful exploration of the localization schemes of Awasthi et al. (2017). We further extend the algorithm and analysis to the more general and stronger nasty noise model of Bshouty et al. (2002), showing that it is still possible to achieve near-optimal noise tolerance and sample complexity in polynomial time.