2023/06/06 by Hyungki Im, Im, Hyungki, Paul Grigas +1 · 1 citation
Computer Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Data Classification
paper · pdf · doi:10.48550/arxiv.2306.03402
openalex publication_date 2023/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Learning with label dependent label noise has been extensively explored in both theory and practice; however, dealing with instance (i.e., feature) and label dependent label noise continues to be a challenging task. The difficulty arises from the fact that the noise rate varies for each instance, making it challenging to estimate accurately. The question of whether it is possible to learn a reliable model using only noisy samples remains unresolved. We answer this question with a theoretical analysis that provides matching upper and lower bounds. Surprisingly, our results show that, without any additional assumptions, empirical risk minimization achieves the optimal excess risk bound. Specifically, we derive a novel excess risk bound proportional to the noise level, which holds in very general settings, by comparing the empirical risk minimizers obtained from clean samples and noisy samples. Second, we show that the minimax lower bound for the 0-1 loss is a constant proportional to the average noise rate. Our findings suggest that learning solely with noisy samples is impossible without access to clean samples or strong assumptions on the distribution of the data.