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.

翻译：针对概率编程的推理算法是包含众多移动部件的复杂命令式程序。高效推理通常需要针对特定概率模型或问题定制算法，这有时被称为推理编程。大多数推理框架使用缺乏对副作用进行规范化处理的语言实现，这可能导致算法结构模糊、推理编程困难的单体式实现。带有类型化效应的函数式编程为可编程推理提供了更具结构化和模块化的基础，其中单子变换器是当前探索的主要结构化机制。本文基于近期利用代数效应表示概率模型的研究成果，提出了一种基于代数效应的可编程推理替代方案。通过使用效应签名来指定算法的关键操作，并借助效应处理器以模块化方式为特定变体解释这些操作，我们开发了三种抽象算法（或称推理模式），分别代表三类重要的推理方法：Metropolis-Hastings算法、粒子滤波算法和引导优化算法。我们展示了该方法如何揭示算法的高层结构，并使得算法各组成部分的定制与重组以生成新变体变得简单易行。我们将这三种推理模式实现为Haskell库，并讨论了代数效应相对于单子变换器作为模块化命令式算法设计结构化机制的优劣。我们提出的库应能在任何能够模拟效应与效应处理器的类型化函数式语言中重新实现。