关于指数族的Rényi和Tsallis熵和发散
On Rényi and Tsallis entropies and divergences for exponential families
摘要：
统计学中许多常见的概率分布，如高斯分布、多项分布、贝塔分布或伽玛分布，都可以在指数族的统一框架下进行研究。在本文中，我们证明了属于同一指数族的分布的Rényi和Tsallis发散都允许一个通用的封闭形式的表达式。此外，我们表明，雷尼和Tsallis熵也可以计算在封闭形式的子族，包括高斯或指数分布，等等。
英文摘要：
Many common probability distributions in statistics like the Gaussian, multinomial, Beta or Gamma distributions can be studied under the unified framework of exponential families. In this paper, we prove that both Rényi and Tsallis divergences of distributions belonging to the same exponential family admit a generic closed form expression. Furthermore, we show that Rényi and Tsallis entropies can also be calculated in closed-form for sub-families including the Gaussian or exponential distributions, among others.
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