List Learning with Attribute Noise
This work addresses a long-standing limitation in PAC learning theory for researchers, but it is incremental as it builds on prior models and results.
The paper tackles the problem of learning with attribute noise by extending it to a list-learning model, showing that sparse conjunctions can be efficiently list-learned under certain distributional assumptions, while proving that efficient learning of parities and majorities remains impossible in this model.
We introduce and study the model of list learning with attribute noise. Learning with attribute noise was introduced by Shackelford and Volper (COLT 1988) as a variant of PAC learning, in which the algorithm has access to noisy examples and uncorrupted labels, and the goal is to recover an accurate hypothesis. Sloan (COLT 1988) and Goldman and Sloan (Algorithmica 1995) discovered information-theoretic limits to learning in this model, which have impeded further progress. In this article we extend the model to that of list learning, drawing inspiration from the list-decoding model in coding theory, and its recent variant studied in the context of learning. On the positive side, we show that sparse conjunctions can be efficiently list learned under some assumptions on the underlying ground-truth distribution. On the negative side, our results show that even in the list-learning model, efficient learning of parities and majorities is not possible regardless of the representation used.