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arXiv · 2003.14145

New approach to greedy vector quantization

Rancy El Nmeir·Harald Luschgy·Gilles Pagès
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Abstract

We extend some rate of convergence results of greedy quantization sequences already investigated in arXiv:1409.0732 [math.PR]. We show, for a more general class of distributions satisfying a certain control, that the quantization error of these sequences have an $n^{-\frac1d}$ rate of convergence and that the distortion mismatch property is satisfied. We will give some non-asymptotic Pierce type estimates. The recursive character of greedy vector quantization allows some improvements to the algorithm of computation of these sequences and the implementation of a recursive formula to quantization-based numerical integration. Furthermore, we establish further properties of sub-optimality of greedy quantization sequences.

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Rancy El Nmeir, Harald Luschgy, Gilles Pagès. 2020-03-31. New approach to greedy vector quantization. https://arxiv.org/abs/2003.14145

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