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)

PDF Abstract

Code


No code implementations yet. Submit your code now

Tasks


Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods used in the Paper


METHOD TYPE
🤖 No Methods Found Help the community by adding them if they're not listed; e.g. Deep Residual Learning for Image Recognition uses ResNet