Fast rates for empirical vector quantization

Clément Levrard

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arXiv · 1201.6052

Fast rates for empirical vector quantization

Clément Levrard

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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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Clément Levrard. 2012-01-29. Fast rates for empirical vector quantization. https://arxiv.org/abs/1201.6052

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