Discrete Gaussian distributions via theta functions

Abstract

We study a discrete analogue of the classical multivariate Gaussian distribution. It is supported on the integer lattice and is parametrized by the Riemann theta function. Over the reals, the discrete Gaussian is characterized by the property of maximizing entropy, just as its continuous counterpart. We capitalize on the theta function representation to derive statistical properties. Throughout, we exhibit strong connections to the study of abelian varieties in algebraic geometry.

23 pages. Final version. To appear in SIAGA. v2: changed notation and added references

References in corpus (3)

• Moment Varieties of Gaussian Mixtures
• Algebraic Identifiability of Gaussian Mixtures
• An Inequality for Gaussians on Lattices

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