Title: Nearest-Neighbor Sample Compression: Efficiency, Consistency, Infinite Dimensions,
Abstract: We examine the Bayes-consistency of a recently proposed
1-nearest-neighbor-based multiclass learning algorithm. This algorithm is
derived from sample compression bounds and enjoys the statistical advantages of
tight, fully empirical generalization bounds, as well as the algorithmic
advantages of a faster runtime and memory savings. We prove that this algorithm
is strongly Bayes-consistent in metric spaces with finite doubling dimension
--- the first consistency result for an efficient nearest-neighbor sample
compression scheme. Rather surprisingly, we discover that this algorithm
continues to be Bayes-consistent even in a certain infinite-dimensional
setting, in which the basic measure-theoretic conditions on which classic
consistency proofs hinge are violated. This is all the more surprising, since
it is known that $k$-NN is not Bayes-consistent in this setting. We pose
several challenging open problems for future research.