Bayesian Networks and Proof-Nets: the proof-theory of Bayesian Inference

TL;DR

This paper explores the relationship between Bayesian Networks and proof-nets in linear logic to develop a proof-theoretical framework for Bayesian inference, emphasizing compositional graphical methods and computational efficiency.

Contribution

It introduces a novel proof-theoretical approach to Bayesian inference using proof-nets, enhancing compositionality and efficiency in graphical representations.

Findings

Establishes a correspondence between Bayesian Networks and proof-nets.

Develops graphical methods for Bayesian inference.

Addresses computational efficiency in proof-theoretic models.

Abstract

We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the Curry-Howard correspondence between proofs and programs), to provide compositional graphical methods, and to take into account computational efficiency. We exploit the fact that the decomposition of a graph is more flexible than that of a proof-tree, or of a type-derivation, even if compositionality becomes more challenging.