On Solutions to Multivariate Maximum -entropy Problems

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 R enyi's -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.