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Fast rates for empirical vector quantization

Clément Levrard 1, 2 
1 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay
2 Laboratoire de probabilités et statistiques d'Orsay
UP11 - Université Paris-Sud - Paris 11
Abstract : We consider the rate of convergence of the expected loss of empirically optimal vector quantizers. Earlier results show that the mean-squared expected distortion for any fixed distribution supported on a bounded set and satisfying some regularity conditions decreases at the rate O(log n/n). We prove that this rate is actually O(1/n). Although these conditions are hard to check, we show that well-polarized distributions with continuous densities supported on a bounded set are included in the scope of this result.
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https://hal.inria.fr/hal-00942672
Contributor : Erwan Le Pennec Connect in order to contact the contributor
Submitted on : Thursday, February 6, 2014 - 11:22:15 AM
Last modification on : Sunday, June 26, 2022 - 12:00:45 PM

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Clément Levrard. Fast rates for empirical vector quantization. Electronic Journal of Statistics , 2013, 7, pp.1716-1746. ⟨10.1214/13-EJS822⟩. ⟨hal-00942672⟩

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