Jun-Iti Nagata
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Related Articles from SNS
Universal consistency of the $k$-NN rule in metric spaces and Nagata dimension. III
Announce Type: replace Abstract: We establish the last missing link allowing to describe those complete separable metric spaces $X$ in which the $k$ nearest neighbour classifier is universally consistent, both in combinatorial terms of dimension theory and via a fundamental property of real analysis. The following are equivalent: (1) The $k$-nearest neighbour classifier is universally consistent in $X$, (2) The strong Lebesgue--Besicovitch differentiation property holds in $X$ for every...