Algebra in probabilistic reasoning

TL;DR

This paper explores how computer algebra can be applied to the implication problem of conditional independence in Gaussian variables, addressing validity certificates, computational complexity, and parallels to automated theorem proving.

Contribution

It introduces the use of computer algebra techniques to analyze conditional independence implications, highlighting their role in research reproducibility and computational complexity.

Findings

Certificates for inference rule validity and invalidity are discussed.

Computational complexity of the inference problem is analyzed.

Connections to automated theorem proving in synthetic geometry are drawn.

Abstract

This short expository paper outlines applications of computer algebra to the implication problem of conditional independence for Gaussian random variables. We touch on certificates for validity and invalidity of inference rules from the perspective of reproducibility of research data, computational complexity of the inference problem and draw a parallel to automated theorem proving in synthetic geometry.