Online Consistency of the Nearest Neighbor Rule
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910678993862656 |
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| author | Dasgupta, Sanjoy So, Geelon |
| author_facet | Dasgupta, Sanjoy So, Geelon |
| contents | In the realizable online setting, a learner is tasked with making predictions for a stream of instances, where the correct answer is revealed after each prediction. A learning rule is online consistent if its mistake rate eventually vanishes. The nearest neighbor rule (Fix and Hodges, 1951) is a fundamental prediction strategy, but it is only known to be consistent under strong statistical or geometric assumptions: the instances come i.i.d. or the label classes are well-separated. We prove online consistency for all measurable functions in doubling metric spaces under the mild assumption that the instances are generated by a process that is uniformly absolutely continuous with respect to a finite, upper doubling measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23644 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Online Consistency of the Nearest Neighbor Rule Dasgupta, Sanjoy So, Geelon Machine Learning In the realizable online setting, a learner is tasked with making predictions for a stream of instances, where the correct answer is revealed after each prediction. A learning rule is online consistent if its mistake rate eventually vanishes. The nearest neighbor rule (Fix and Hodges, 1951) is a fundamental prediction strategy, but it is only known to be consistent under strong statistical or geometric assumptions: the instances come i.i.d. or the label classes are well-separated. We prove online consistency for all measurable functions in doubling metric spaces under the mild assumption that the instances are generated by a process that is uniformly absolutely continuous with respect to a finite, upper doubling measure. |
| title | Online Consistency of the Nearest Neighbor Rule |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.23644 |