  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.
