On Solutions to Multivariate Maximum alpha-Entropy Problems
On Solutions to Multivariate Maximum alpha-Entropy Problems
复制标题
关于多元最大α熵问题的解
DOI：
10.1007/978-3-540-45063-4_14
复制
发表时间：
2003
影响因子：
2.5
通讯作者：
C. Vignat
中科院分区：
文献类型：
--
作者：
Jose A. Costa;A. Hero;C. Vignat
在计算机视觉和模式识别中，熵被广泛用作问题的优化函数。为了深入了解这些方法，重要的是要表征由熵优化产生的最大熵概率分布的行为。本文的目的是在协方差约束下，建立一类称为Renyi‘sα-熵的一般熵函数的最大熵多元分布的性质。首先，我们证明了这些熵最大化的分布表现出有趣的性质，例如球不变性，并且具有随机的高斯-伽马混合表示。然后，我们转向加法下熵最大化分布类的稳定性问题。
Entropy has been widely employed as an optimization function for problems in computer vision and pattern recognition. To gain insight into such methods it is important to characterize the behavior of the maximum-entropy probability distributions that result from the entropy optimization. The aim of this paper is to establish properties of multivariate distributions maximizing entropy for a general class of entropy functions, called Renyi’s α-entropy, under a covariance constraint. First we show that these entropy-maximizing distributions exhibit interesting properties, such as spherical invariance, and have a stochastic Gaussian-Gamma mixture representation. We then turn to the question of stability of the class of entropy-maximizing distributions under addition.