Probabilistic Inference Using Generators - The Statues Algorithm

TL;DR

The paper introduces the Statues algorithm, an exact probabilistic inference method for discrete models like Bayesian networks, offering efficiency improvements and practical Python implementations.

Contribution

It presents the Statues algorithm, a novel variable binding-based inference method that improves efficiency for exact marginal probability calculations in discrete probabilistic models.

Findings

Efficient exact marginalization for discrete probabilistic models.

Implementation of the algorithm in Python libraries Lea and MicroLea.

Demonstrated use cases validating the algorithm's effectiveness.

Abstract

We present here a new probabilistic inference algorithm that gives exact results in the domain of discrete probability distributions. This algorithm, named the Statues algorithm, calculates the marginal probability distribution on probabilistic models defined as direct acyclic graphs. These models are made up of well-defined primitives that allow to express, in particular, joint probability distributions, Bayesian networks, discrete Markov chains, conditioning and probabilistic arithmetic. The Statues algorithm relies on a variable binding mechanism based on the generator construct, a special form of coroutine; being related to the enumeration algorithm, this new algorithm brings important improvements in terms of efficiency, which makes it valuable in regard to other exact marginalization algorithms. After introduction of several definitions, primitives and compositional rules, we present in details the Statues algorithm. Then, we briefly discuss the interest of this algorithm compared to others and we present possible extensions. Finally, we introduce Lea and MicroLea, two Python libraries implementing the Statues algorithm, along with several use cases. A proof of the correctness of the algorithm is provided in appendix.