一种新的贪婪矢量量化方法
New approach to greedy vector quantization
摘要：
我们扩展了在arXiv：1409.0732 [math.PR]中已经研究的贪婪量化序列的一些收敛速率结果。我们表明，对于一个更一般的类的分布，满足一定的控制，这些序列的量化误差有一个$n^{-\frac1d}$收敛速率和失真失配属性是满意的。我们将给出一些非渐近Pierce型估计。贪婪矢量量化的递归特性允许对这些序列的计算算法进行一些改进，并将递归公式实现到基于量化的数值积分。此外，我们建立了贪婪量化序列的次优性的进一步性质。
英文摘要：
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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