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Universal consistency and rates of convergence of multiclass prototype algorithms in metric spaces.
- Source :
-
Journal of Machine Learning Research . 2021, Vol. 22, p1-25. 25p. - Publication Year :
- 2021
-
Abstract
- We study universal consistency and convergence rates of simple nearest-neighbor prototype rules for the problem of multiclass classification in metric spaces. We first show that a novel data-dependent partitioning rule, named Proto-NN, is universally consistent in any metric space that admits a universally consistent rule. Proto-NN is a significant simplification of OptiNet, a recently proposed compression-based algorithm that, to date, was the only algorithm known to be universally consistent in such a general setting. Practically, Proto-NN is simpler to implement and enjoys reduced computational complexity. We then proceed to study convergence rates of the excess error probability. We first obtain rates for the standard k-NN rule under a margin condition and a new generalized-Lipschitz condition. The latter is an extension of a recently proposed modified-Lipschitz condition from Rd to metric spaces. Similarly to the modified-Lipschitz condition, the new condition avoids any boundness assumptions on the data distribution. While obtaining rates for Proto-NN is left open, we show that a second prototype rule that hybridizes between k-NN and Proto-NN achieves the same rates as k-NN while enjoying similar computational advantages as Proto-NN. However, as k-NN, this hybrid rule is not consistent in general. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15324435
- Volume :
- 22
- Database :
- Academic Search Index
- Journal :
- Journal of Machine Learning Research
- Publication Type :
- Academic Journal
- Accession number :
- 155404688