Hybrid Method for Optimal Quantization of the Normal Distribution
Sana Ben Hamida · Open Transactions on Information Processing · 2014
Quantization of a continuous-value signal into discrete form is a standard task in all analog/digital devices commonly used to solve numerical problems in finance. In this paper, we consider quantization of the Normal distribution. We suggest an hybrid technique based on the evolutionary optimization and the Stochastic Gradient for obtaining an optimal Lp-quantizer of a multidimensional random variable. First, we present the classical gradient-based approach used up to now to find a near optimal Lp-quantizer which is frequently used to solve some high dimensional problems arising in finance. Then, we give an algorithm that permits to deal with the problem in the evolutionary optimization framework. Otherwise, to improve the capacity of the algorithm to fine-tune the best found solutions, we propose an hybrid method combining the two techniques. The objective of the hybrid method is to allow an powerful exploration and exploitation of the problem search space. The effectiveness of the proposed method is demonstrated throw numerical experiments.