Learning with metric losses.

Dan Tsir Cohen, Aryeh Kontorovich

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We propose a practical algorithm for learning mappings between two metric spaces, \X and \Y. Our procedure is strongly Bayes-consistent whenever \X and \Y are topologically separable and \Y 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 Fréchet 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 {\em semi-stable compression}, which may be of independent interest.
Original languageEnglish
Title of host publicationCOLT
Pages662-700
Number of pages39
StatePublished - 2022

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