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 holomorphic theta function. In this work, we present formula for several common statistical divergences between discrete normal distributions including the Kullback-Leibler divergence. In particular, we describe an efficient approximation technique for approximating the Kullback-Leibler divergence between discrete normal distributions via the $\gamma$-divergences.

翻译：分解正常分布的定义是,以规定的方式和共变矩阵进行分配,在整数衬垫支持上实现最大倍增。一组离散正常分布形成指数式组合,与Riemann holormophic 等函数相关,具有累积功能。在这项工作中,我们提出了离散正常分布之间若干共同统计差异的公式,包括 Kullback- Leiber 差异。特别是,我们描述了一种高效近似技术,通过 $\ gamma$- diverences 来接近 Kullback- Lebeler 的离散正常分布差异。