Lazy Factored Inference for Functional Probabilistic Programming

TL;DR

This paper introduces lazy factored inference, a novel approach that enables factored algorithms to perform inference on probabilistic programs with infinitely many variables by expanding models to a bounded depth and bounding the unexpanded parts.

Contribution

The paper presents a new inference framework, lazy factored inference, that extends factored algorithms to handle infinite probabilistic models in programming languages.

Findings

Enables inference on models with infinitely many variables.

Provides bounds on query probabilities using partial model expansion.

Integrates program structure to improve inference accuracy.

Abstract

Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored inference algorithms are widely used for probabilistic graphical models, but cannot be applied to these programs because all the variables and factors have to be enumerated. In this paper, we present a new inference framework, lazy factored inference (LFI), that enables factored algorithms to be used for models with infinitely many variables. LFI expands the model to a bounded depth and uses the structure of the program to precisely quantify the effect of the unexpanded part of the model, producing lower and upper bounds to the probability of the query.