Learning and decision-making in domains with naturally high noise-to-signal ratios - such as Finance or Healthcare - is often challenging, while the stakes are very high. In this paper, we study the problem of learning and acting under a general noisy generative process. In this problem, the data distribution has a significant proportion of uninformative samples with high noise in the label, while part of the data contains useful information represented by low label noise. This dichotomy is present during both training and inference, which requires the proper handling of uninformative data during both training and testing. We propose a novel approach to learning under these conditions via a loss inspired by the selective learning theory. By minimizing this loss, the model is guaranteed to make a near-optimal decision by distinguishing informative data from uninformative data and making predictions. We build upon the strength of our theoretical guarantees by describing an iterative algorithm, which jointly optimizes both a predictor and a selector, and evaluates its empirical performance in a variety of settings.

Label noise is frequently observed in real-world large-scale datasets. The noise is introduced due to a variety of reasons; it is heterogeneous and feature-dependent. Most existing approaches to handling noisy labels fall into two categories: they either assume an ideal feature-independent noise, or remain heuristic without theoretical guarantees. In this paper, we propose to target a new family of featuredependent label noise, which is much more general than commonly used i.i.d. Focusing on this general noise family, we propose a progressive label correction algorithm that iteratively corrects labels and refines the model. We provide theoretical guarantees showing that for a wide variety of (unknown) noise patterns, a classifier trained with this strategy converges to be consistent with the Bayes classifier. In experiments, our method outperforms SOTA baselines and is robust to various noise types and levels. Addressing noise in training set labels is an important problem in supervised learning. Incorrect annotation of data is inevitable in large-scale data collection, due to intrinsic ambiguity of data/class and mistakes of human/automatic annotators (Yan et al., 2014; Andreas et al., 2017). Developing methods that are resilient to label noise is therefore crucial in real-life applications.