Probabilistic Programming with Stochastic Probabilities

We present a new approach to the design and implementation of probabilistic programming languages (PPLs), based on idea stochastically estimating probability density ratios necessary for inference. By relaxing usual PPL constraint that these densities be computed exactly, we are able eliminate many common restrictions in current PPLs, deliver language that, first time, simultaneously supports first-class constructs marginalization nested inference, unrestricted stochastic control flow, continuous discrete sampling, programmable inference with custom proposals. At heart our is technique compiling expressive programs into randomized algorithms unbiasedly their reciprocals. employ estimators within modified Monte Carlo guaranteed sound despite reliance inexact estimates ratios. establish correctness compiler using logical relations over semantics λ SP , core calculus modeling probabilities. also implement an open-source extension Gen, called GenSP, evaluate it six challenging problems adapted from literature. find that: (1) ‍can automate fast very expensive exact densities; (2) convergence mostly unaffected by noise estimators; (3) sound-by-construction competitive hand-coded estimators, incurring only small constant-factor overhead.