Universal Bayes consistency in metric spaces

24 Jun 2019Steve HannekeAryeh KontorovichSivan SabatoRoi Weiss

We extend a recently proposed 1-nearest-neighbor-based multiclass learning algorithm and prove that our modification is universally strongly Bayes-consistent in all metric spaces admitting {\em any} such learner, making it an ``optimistically universal'' Bayes-consistent learner. This is the first learning algorithm known to enjoy this property; by comparison, the $k$-NN classifier and its variants are not generally universally Bayes-consistent, except under additional structural assumptions, such as an inner product, a norm, finite dimension, or a Besicovitch-type property... (read more)

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