Reactive Graphs for Efficient Markov Chain Monte Carlo Inference in Probabilistic Programming Languages

Abstract: An important aspect of making inference based on a probabilistic program practical is efficiency; faster evaluation enables more work per unit of time, which can be translated into more precision. Inference via Markov chain Monte Carlo has a property that can be favorably exploited for efficiency: most proposed samples are computed as minor variations of previous samples, i.e., a clever implementation can skip computations pertaining to what is unchanged. This paper provides an approach for automatically translating a probabilistic program to a dynamic graph, reminiscent of functional reactive programming, that explicitly represents data dependencies, enabling proposals to only recompute the parts of the graph that depend on redrawn random variables. The graph-building interface follows familiar functional programming interfaces, which also connect to their expressiveness in terms of probabilistic programming: models using the applicative functor portion express Bayesian networks, while those using monads represent universal probabilistic programming languages.