# Compositional Inference Metaprogramming with Convergence Guarantees

## TL;DR

This paper introduces a formal framework for probabilistic inference metaprogramming that guarantees convergence of hybrid algorithms applying different MCMC methods to subproblems, advancing the theoretical understanding of probabilistic programming.

## Contribution

It presents the first formal convergence guarantees for hybrid probabilistic inference algorithms using subproblem-based metaprogramming.

## Key findings

- Proves asymptotic convergence for inference metaprogramming with hybrid algorithms.
- Defines independent subproblem inference and its advantages.
- Establishes a mathematical framework for analyzing convergence in probabilistic programming.

## Abstract

Inference metaprogramming enables effective probabilistic programming by supporting the decomposition of executions of probabilistic programs into subproblems and the deployment of hybrid probabilistic inference algorithms that apply different probabilistic inference algorithms to different subproblems. We introduce the concept of independent subproblem inference (as opposed to entangled subproblem inference in which the subproblem inference algorithm operates over the full program trace) and present a mathematical framework for studying convergence properties of hybrid inference algorithms that apply different Markov-Chain Monte Carlo algorithms to different parts of the inference problem. We then use this formalism to prove asymptotic convergence results for probablistic programs with inference metaprogramming. To the best of our knowledge this is the first asymptotic convergence result for hybrid probabilistic inference algorithms defined by (subproblem-based) inference metaprogramming.