Joudeh Basheer, Škorić Boris
Department of Computer Science and Mathematics, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands.
Entropy (Basel). 2024 Aug 1;26(8):659. doi: 10.3390/e26080659.
We calculate the average differential entropy of a -component Gaussian mixture in Rn. For simplicity, all components have covariance matrix σ21, while the means {Wi}i=1q are i.i.d. Gaussian vectors with zero mean and covariance s21. We obtain a series expansion in μ=s2/σ2 for the average differential entropy up to order O(μ2), and we provide a recipe to calculate higher-order terms. Our result provides an analytic approximation with a quantifiable order of magnitude for the error, which is not achieved in previous literature.
我们计算了(n)维空间中(q)分量高斯混合的平均微分熵。为简单起见，所有分量的协方差矩阵均为(\sigma^{2}I)，而均值({\mathbf{w}i}{i = 1}^q)是独立同分布的高斯向量，均值为零，协方差为(s^{2}I)。我们得到了平均微分熵在(\mu = s^{2}/\sigma^{2})下直至(O(\mu^{2}))阶的级数展开式，并给出了计算高阶项的方法。我们的结果提供了一种具有可量化误差量级的解析近似，这是以往文献中未实现的。
