The course aims to give students the tools to represent and reason about uncertainty using Bayesian networks, and to then situate this formalism within the broader language of category theory.
Prerequisiti
Basic propositional and predicate logic (syntax, semantics, logical consequence). Basic probability theory (discrete probability spaces, conditional probability, independence). Elementary set theory and algebra (relations, functions, basic algebraic structures).
Metodi didattici
This course has two main parts: lectures and exercises. Programming will not be part of this course.
Verifica Apprendimento
The exam is written.
Testi
The course is based on a set of notes that are supplemented by a selection of articles and books.
Contenuti
Logical and semantic foundations of probabilistic reasoning; Bayesian networks, conditional independence, and inference. Basic category theory: categories, functors, monoidal structure. Markov categories as a categorical formalization of conditional probability, with translation between Bayesian networks and their categorical counterparts.
