Rates of convergence for nearest neighbor classification

Advances in Neural Information Processing Systems

Volumn 4, Issue January, 2014, Pages 3437-3445

  Chaudhuri, Kamalika ^a   Dasgupta, Sanjoy ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SAMPLING;

CONVERGENCE RATES; NEAREST NEIGHBOR CLASSIFICATION; NEAREST NEIGHBOR MATCH; NEAREST NEIGHBORS; NONPARAMETRIC CLASSIFICATION; RATES OF CONVERGENCE; UNIVERSAL CONSISTENCY; UPPER AND LOWER BOUNDS;

INFORMATION SCIENCE;

EID: 84937911938     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. J.-Y. Audibert and A.B. Tsybakov. Fast learning rates for plug-in classifiers. Annals of Statistics, 35(2): 608-633, 2007.
2. T. Cover and P.E. Hart. Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13: 21-27, 1967.
3. T.M. Cover. Rates of convergence for nearest neighbor procedures. In Proceedings of The Hawaii International Conference on System Sciences, 1968.
4. S. Dasgupta. Consistency of nearest neighbor classification under selective sampling. In Twenty-Fifth Conference on Learning Theory, 2012.
5. L. Devroye, L. Gyorfi, A. Krzyzak, and G. Lugosi. On the strong universal consistency of nearest neighbor regression function estimates. Annals of Statistics, 22: 1371-1385, 1994.
6. H. Federer. Geometric Measure Theory. Springer, 1969.
7. E. Fix and J. Hodges. Discriminatory analysis, nonparametric discrimination. USAF School of Aviation Medicine, Randolph Field, Texas, Project 21-49-004, Report 4, Contract AD41(128)-31, 1951.
8. J. Fritz. Distribution-free exponential error bound for nearest neighbor pattern classification. IEEE Transactions on Information Theory, 21(5): 552-557, 1975.
9. L. Gyorfi. The rate of convergence of kn-nn regression estimates and classification rules. IEEE Transactions on Information Theory, 27(3): 362-364, 1981.
10. J. Heinonen. Lectures on Analysis on Metric Spaces. Springer, 2001.
11. R. Kaas and J.M. Buhrman. Mean, median and mode in binomial distributions. Statistica Neerlandica, 34(1): 13-18, 1980.
12. S. Kulkarni and S. Posner. Rates of convergence of nearest neighbor estimation under arbitrary sampling. IEEE Transactions on Information Theory, 41(4): 1028-1039, 1995.
13. E. Mammen and A.B. Tsybakov. Smooth discrimination analysis. The Annals of Statistics, 27(6): 1808-1829, 1999.
14. E. Slud. Distribution inequalities for the binomial law. Annals of Probability, 5: 404-412, 1977.
15. C. Stone. Consistent nonparametric regression. Annals of Statistics, 5: 595-645, 1977.
16. A.B. Tsybakov. Optimal aggregation of classifiers in statistical learning. The Annals of Statistics, 32(1): 135-166, 2004.
17. R. Urner, S. Ben-David, and S. Shalev-Shwartz. Access to unlabeled data can speed up prediction time. In International Conference on Machine Learning, 2011.
18. T.J. Wagner. Convergence of the nearest neighbor rule. IEEE Transactions on Information Theory, 17(5): 566-571, 1971.