Scaling Integer Arithmetic in Probabilistic Programs

These approximate inference strategies can scale well in many cases, but they Distributions on integers are ubiquitous in probabilistic struggle to find valid sampling regions in the presence of modeling but remain challenging for many low-probability observations and non-differentiability (e.g., of today's probabilistic programming languages observing the sum of two large random integers to be a (PPLs). The core challenge comes from discrete constant) [Gelman et al., 2015, Bingham et al., 2019, Dillon structure: many of today's PPL inference strategies et al., 2017]. Exact inference strategies work by preserving rely on enumeration, sampling, or differentiation the global structure of the distribution, but here there is a in order to scale, which fail for high-dimensional challenge: what is the right strategy for efficiently representing complex discrete distributions involving integers.