论文标题
贪婪矢量量化的新方法
New approach to greedy vector quantization
论文作者
论文摘要
我们扩展了在ARXIV中已经研究的贪婪量化序列的收敛结果：1409.0732 [Math.pr]。我们显示，对于满足某个控件的更一般的分布类别，这些序列的量化误差具有$ n^{ - \ frac1d} $收敛速率，并且满足了失真不匹配属性。我们将给出一些非反应的Pierce类型估计。贪婪矢量量化的递归特征允许对这些序列的计算算法进行一些改进，并实现了基于量化的数值集成的递归公式。此外，我们建立了贪婪量化序列的亚次优先性的进一步特性。
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.
