The Kullback–Leibler Divergence Between Lattice Gaussian Distributions

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