Discrete normal distributions are defined as the distributions with prescribed means and covariance matrices which maximize entropy on the integer lattice support. The set of discrete normal distributions form an exponential family with cumulant function related to the Riemann theta function. In this paper, we present several formula for common statistical divergences between discrete normal distributions including the Kullback-Leibler divergence. In particular, we describe an efficient approximation technique for calculating the Kullback-Leibler divergence between discrete normal distributions via the R\'enyi $\alpha$-divergences or the projective $\gamma$-divergences.

翻译：分解的正常分布被定义为以规定的方式和共变矩阵进行分配,这些分布在整数衬垫支持上能最大限度地增加酶。一组离散的正常分布构成一个指数式组合,与Riemann theta 函数相关,具有累积函数。在本文件中,我们为离散的正常分布之间的共同统计差异提出了几种公式,包括 Kullback- Leiber 差异。特别是,我们描述一种高效近似技术,通过 R\'enyi $\ alpha$- divegences 或 progive $\gmam$- divegences 计算离散正常分布之间的 Kullback- Leber差 。