## Claudia Faggian (CNRS - IRIF), Bayesian Networks and Proof Nets: Curry-Howard meets Bayes

### Schedule

- Sept. 22, 2022, 15:00 - 16:00

### Abstract

(joint work with Thomas Ehrhard and Michele Pagani )

This talk proposes a proof-theoretical account of Bayesian Inference, by uncovering a close correspondence between two graphical languages, namely Bayesian Networks and Proof Nets. The former is a prominent graphical model for probabilistic reasoning. The latter is a graph formalism for Linear Logic proofs and (via the Curry-Howard correspondence of proofs as programs) a powerful tool to analyze the dynamics of proof/the execution of programs. Their natural interpretation into Probabilistic Coherence Spaces makes Proof Nets into probabilistic models.

The correspondence which we develop involves both the
*representation* and the *computation* of a probabilistic model. In
particular, we relate the most widely used algorithm for exact
inference (message passing over clique trees) with the inductive
interpretation of a proof, opportunely factorized into a composition of
smaller proofs. The correspondence turns out to be so tight, that even
the computational cost of inference is similar. We will also discuss
some of the perspectives which proof theory could bring, such as
compositionality (via types) and structure (hierarchical models).