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Optimal rates for $k$-NN density and mode estimation
Post-edited
Authors : Kpotufe, Samory (Author of the conference)
CIRM (Publisher )
62G07 - Density estimation
CIRM (Publisher )
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| mean-shift procedure $k$-NN density estimate rate for $k$-NN density estimates single mode rate multiple modes rate multiple modes estimation pruning bad modes questions |
Abstract :
We present two related contributions of independent interest: high-probability finite sample rates for $k$-NN density estimation, and practical mode estimators – based on $k$-NN – which attain minimax-optimal rates under surprisingly general distributional conditions.
$k$-nearest neighbor ($k$-NN) - $k$-NN density rates - mode estimation
MSC Codes : $k$-nearest neighbor ($k$-NN) - $k$-NN density rates - mode estimation
62G07 - Density estimation
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 08/01/15 Conference Date : 16/12/14 Subseries : Research talks arXiv category : Machine Learning Mathematical Area(s) : Computer Science ; Probability & Statistics Format : QuickTime (.mov) Video Time : 00:31:27 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-12-16_Kpotufe.mp4 
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Information on the Event
Event Title : Meeting in mathematical statistics: new procedures for new data / Rencontre de statistiques mathématiques : nouvelles procédures pour de nouvelles donnéesEvent Organizers : Pouet, Christophe ; Reiss, Markus ; Rigollet, Philippe Dates : 15/12/14 - 19/12/14 Event Year : 2014
Citation Data
DOI : 10.24350/CIRM.V.18658803Cite this video as: Kpotufe, Samory (2014). Optimal rates for $k$-NN density and mode estimation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18658803 URI : http://dx.doi.org/10.24350/CIRM.V.18658803 |
Bibliography
- Abraham, C., Biau, G., & Cadre, B. (2004). On the asymptotic properties of a simple estimate of the mode. European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics, 8, 1-11 - http://dx.doi.org/10.1051/ps:2003015
- Biau, G., Chazal, F., Cohen-Steiner, D., Devroye, L., & Rodríguez, C. (2011). A weighted $k$-nearest neighbor density estimate for geometric inference. Electronic Journal of Statistics, 5, 204-237 - http://dx.doi.org/10.1214/11-EJS606
- Chaudhuri, K., Dasgupta, S., Kpotufe, S. & von Luxburg, U. (2014). Consistent procedures for cluster tree estimation and pruning.
- Dasgupta, S., & Kpotufe, S. (2014). Optimal rates for $k$-NN density and mode estimation. In Z. Ghahramani, M. Welling, C. Cortes, N.D. Lawrence, & K.Q. Weinberger (Eds.), Advances in Neural Information Processing Systems 27 (pp. 2555-2563). New-York: Curran Associates - http://papers.nips.cc/paper/5387-optimal-rates-for-k-nn-density-and-mode-estimation.pdf
- Devroye, L.P., & Wagner, T.J. (1977).The strong uniform consistency of nearest neighbor density estimates.The Annals of Statistics, 5, 536-540 - http://projecteuclid.org/euclid.aos/1176343851
- Devroye, L. (1979). Recursive estimation of the mode of a multivariate density. Canadian Journal of Statistics, 7(2), 159-167 - http://dx.doi.org/10.2307/3315115
- Genovese, C., Perone-Pacifico, M., Verdinelli, I., & Wasserman, L. (2013) Nonparametric inference for density modes.
- Moore, D.S., & Yackel, J.W. (1976). Large sample properties of nearest neighbor density function estimators. In S.S. Gupta & D.S. Moore (Eds.) Statistical decision theory and related topics. II. Proceedings of a symposium held at Purdue University, West Lafayette/Indiana, May 17-19, 1976 (pp. 269-279). New-York: Academic Press - https://www.zbmath.org/?q=an:0409.00010
- Tsybakov, A.B. (1990). Recursive estimation of the mode of a multivariate distribution. Problems of Information Transmission, 26(1), 31-37 -
