Paolo Perrone - Markov Categories and Entropy

Talk at Applied Category Theory 2023 Markov categories are a novel framework to describe and treat problems in probability and information theory. One can combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and data processing inequalities. Several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric. For instance, Markov categories give a notion of determinism for sources and channels, and we can define entropy exactly by measuring how far a source or channel is from being deterministic. This recovers Shannon and Rényi entropies, as well as the Gini-Simpson index used in ecology to quantify diversity, and it can be used to give a conceptual definition of generalized entropy. https://act2023.github.io/ https://act2023.github.io/papers/pape...