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.

Trace types and denotational semantics for sound programmable inference in probabilistic languages

“…Shuffle [Atkinson et al 2018] features a type system for verifying hand-coded Monte Carlo inference algorithms, but its focus is not on algorithms that use custom proposal distributions, but rather algorithms that explicitly manipulate densities, or exploit analytic relationships in a model to marginalize out nuisance variables. Shuffle, and earlier systems like BLAISE [Bonawitz 2008] and AugurV2 [Huang et al 2017], have introduced sound combinators for MCMC kernels, much like the ones we present here. The novelty in our work on kernel combinators comes from two places: (1) our kernels track, in their types, the class of models for which they are stationary, and 2we introduce a combinator, if K , for conditional execution, which is only guaranteed to be sound because the type ensures that the condition for execution cannot be negated by the kernel being executed.…”

Reactive probabilistic programming

“…Over the last few years there has been a growing interest on probabilistic programming languages. Some languages like BUGS [25], Stan [9], or Augur [21] offer optimized inference technique for a constrained subset of models. Other languages like WebPPL [18], Edward [37], Pyro [6], or Birch [28] focus on expressivity allowing the specification of arbitrary complex models.…”

Gen: a general-purpose probabilistic programming system with programmable inference

“…Inference Implementation Efficiency For efficient implementation of MCMC or MAP updates that act on a subset of variables in a model, many probabilistic programming systems (including Gen) incrementally compute probability ratios and trace updates [29,40,51,69]. However, existing systems either lack Gen's modeling flexibility [29], are restricted to single-variable updates [51,69], and/or have very high runtime overhead [40]. Gen's use of static analysis, JIT compilation, generative function combinators, and argdiffs provides a unique combination of implementation efficiency and flexibility of updates.…”