Categorical Probability and Information Theory
Speaker: Paolo Perrone (University of Oxford)Date: Tuesday, 09 May 2023 - 13:00Place: Room 2.2.D08, Universidad Carlos III de Madrid
Markov categories are a modern framework designed to deal with uncertainty and probability in terms of category theory. Most conceptual aspects of probability theory can be described naturally in this way, for example stochastic dependence and independence, conditioning, and conditional independence. More importantly, several theorems of probability and information theory have been recently stated, intepreted, and even proven, purely in terms of Markov categories. Among them we have the de Finetti theorem, the ergodic decomposition theorem, and a general theory of graphical models. In addition, several concepts of classical information theory, such as the notions of entropy and mutual information, and the data processing inequalities that they satisfy, can be studied using Markov categories, and can be recovered from enriched categorical principles. In this talk we give an overview of some of the concepts and results of the theory, and introduce its intrinsic graphical language.