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Journal Articles Electronic Journal of Statistics Year : 2013

Fast rates for empirical vector quantization

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.

Dates and versions

hal-00942672 , version 1 (06-02-2014)

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Cite

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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