Effects and Effect Handlers for Programmable Inference

Inference algorithms for probabilistic programming are complex imperative programs with many moving parts. Efficient inference often requires customising an algorithm to a particular probabilistic model or problem, sometimes called inference programming. Most inference frameworks are implemented in languages that lack a disciplined approach to side effects, which can result in monolithic implementations where the structure of the algorithms is obscured and inference programming is hard. Functional programming with typed effects offers a more structured and modular foundation for programmable inference, with monad transformers being the primary structuring mechanism explored to date. This paper presents an alternative approach to programmable inference, based on algebraic effects, building on recent work that used algebraic effects to represent probabilistic models. Using effect signatures to specify the key operations of the algorithms, and effect handlers to modularly interpret those operations for specific variants, we develop three abstract algorithms, or inference patterns, representing three important classes of inference: Metropolis-Hastings, particle filtering, and guided optimisation. We show how our approach reveals the algorithms' high-level structure, and makes it easy to tailor and recombine their parts into new variants. We implement the three inference patterns as a Haskell library, and discuss the pros and cons of algebraic effects vis-a-vis monad transformers as a structuring mechanism for modular imperative algorithm design. It should be possible to reimplement our library in any typed functional language able to emulate effects and effect handlers.