Compiling Markov chain Monte Carlo algorithms for probabilistic modeling

Abstract

The problem of probabilistic modeling and inference, at a high-level, can be viewed as constructing a ( model , query , inference ) tuple, where an inference algorithm implements a query on a model . Notably, the derivation of inference algorithms can be a difficult and error-prone task. Hence, researchers have explored how ideas from probabilistic programming can be applied. In the context of constructing these tuples, probabilistic programming can be seen as taking a language-based approach to probabilistic modeling and inference. For instance, by using (1) appropriate languages for expressing models and queries and (2) devising inference techniques that operate on encodings of models (and queries) as program expressions, the task of inference can be automated. In this paper, we describe a compiler that transforms a probabilistic model written in a restricted modeling language and a query for posterior samples given observed data into a Markov Chain Monte Carlo (MCMC) inference algorithm that implements the query. The compiler uses a sequence of intermediate languages (ILs) that guide it in gradually and successively refining a declarative specification of a probabilistic model and the query into an executable MCMC inference algorithm. The compilation strategy produces composable MCMC algorithms for execution on a CPU or GPU.