连续型随机向量联合熵的离散方差分离估计

提出了一种"离散方差分离"法,用于连续型随机向量联合熵的估计.方法分为"方差分离"和"离散"两个步骤.前者通过分离"标准熵"与"标准差对数和"来避免维数灾害;后者通过各分量的"最佳分割数"来离散连续型随机向量,从而避开了联合密度估计.仿真实验表明:该方法以很低的计算复杂度,准确地逼近了理论值.

A Discrete Variance Separation Estimation to the Joint Entropy of Continuous Random Vector

A new method named Discrete Variance Separation(DVS) is proposed in this paper to estimate the joint entropy of continuous random vector.This method can be separated into two steps.The first step referred to as"variance separation"divides the joint entropies into standard entropy and the sum of the logarithm of standard deviations in order to prevent the curse of dimension.The second step called"discretization"estimates the standard entropy,which discretizes continuous random vectors by the best partition numbers of their elements so that bypasses the estimation of joint density.Simulated experiments show that results from this new method approach the theoretic values with high accuracy and computation complexity.