Metric-valued regression

Abstract

We propose an efficient algorithm for learning mappings between two metric spaces, and . Our procedure is strongly Bayes-consistent whenever and are topologically separable and is "bounded in expectation" (our term; the separability assumption can be somewhat weakened). At this level of generality, ours is the first such learnability result for unbounded loss in the agnostic setting. Our technique is based on metric medoids (a variant of Fr\'echet means) and presents a significant departure from existing methods, which, as we demonstrate, fail to achieve Bayes-consistency on general instance- and label-space metrics. Our proofs introduce the technique of semi-stable compression, which may be of independent interest.

Tasks

Reproductions