Stochastically Differentiable Probabilistic Programs
This addresses a key bottleneck in probabilistic programming systems for researchers and practitioners, offering a more efficient and automated solution for mixed-support models.
The paper tackles the challenge of performing gradient-based inference in probabilistic programs with mixed continuous and discrete latent variables, which existing methods handle inefficiently or require manual effort. It introduces a stochastic gradient MCMC approach that outperforms baselines, achieving performance close to marginalized versions with less programming and computational cost.
Probabilistic programs with mixed support (both continuous and discrete latent random variables) commonly appear in many probabilistic programming systems (PPSs). However, the existence of the discrete random variables prohibits many basic gradient-based inference engines, which makes the inference procedure on such models particularly challenging. Existing PPSs either require the user to manually marginalize out the discrete variables or to perform a composing inference by running inference separately on discrete and continuous variables. The former is infeasible in most cases whereas the latter has some fundamental shortcomings. We present a novel approach to run inference efficiently and robustly in such programs using stochastic gradient Markov Chain Monte Carlo family of algorithms. We compare our stochastic gradient-based inference algorithm against conventional baselines in several important cases of probabilistic programs with mixed support, and demonstrate that it outperforms existing composing inference baselines and works almost as well as inference in marginalized versions of the programs, but with less programming effort and at a lower computation cost.