Adaptive density estimation for clustering with gaussian mixtures

C. Maugis-Rabusseau; B. Michel

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 698-724
  • ISSN: 1292-8100

Abstract

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Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum likelihood estimator is proposed for automatically selecting the number of mixture components. In the present paper, a collection of univariate densities whose logarithm is locally β-Hölder with moment and tail conditions are considered. We show that this penalized estimator is minimax adaptive to the β regularity of such densities in the Hellinger sense.

How to cite

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Maugis-Rabusseau, C., and Michel, B.. "Adaptive density estimation for clustering with gaussian mixtures." ESAIM: Probability and Statistics 17 (2013): 698-724. <http://eudml.org/doc/273632>.

@article{Maugis2013,
abstract = {Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum likelihood estimator is proposed for automatically selecting the number of mixture components. In the present paper, a collection of univariate densities whose logarithm is locally β-Hölder with moment and tail conditions are considered. We show that this penalized estimator is minimax adaptive to the β regularity of such densities in the Hellinger sense.},
author = {Maugis-Rabusseau, C., Michel, B.},
journal = {ESAIM: Probability and Statistics},
keywords = {rate adaptive density estimation; gaussian mixture clustering; hellinger risk; non asymptotic model selection; Gaussian mixture clustering; Hellinger risk},
language = {eng},
pages = {698-724},
publisher = {EDP-Sciences},
title = {Adaptive density estimation for clustering with gaussian mixtures},
url = {http://eudml.org/doc/273632},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Maugis-Rabusseau, C.
AU - Michel, B.
TI - Adaptive density estimation for clustering with gaussian mixtures
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 698
EP - 724
AB - Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum likelihood estimator is proposed for automatically selecting the number of mixture components. In the present paper, a collection of univariate densities whose logarithm is locally β-Hölder with moment and tail conditions are considered. We show that this penalized estimator is minimax adaptive to the β regularity of such densities in the Hellinger sense.
LA - eng
KW - rate adaptive density estimation; gaussian mixture clustering; hellinger risk; non asymptotic model selection; Gaussian mixture clustering; Hellinger risk
UR - http://eudml.org/doc/273632
ER -

References

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  14. [14] C. Maugis and B. Michel, Adaptive density estimation for clustering with Gaussian mixtures (2011). arXiv:1103.4253v2. Zbl06282493
  15. [15] C. Maugis and B. Michel, Data-driven penalty calibration: a case study for Gaussian mixture model selection. ESAIM: PS 15 (2011) 320–339. Zbl06157520MR2870518
  16. [16] C. Maugis and B. Michel, A non asymptotic penalized criterion for Gaussian mixture model selection. ESAIM: PS 15 (2011) 41–68. Zbl06157507MR2870505
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