3 citations · 3 across the 4 of their papers we have counts for
9 papers
Involutive Markov categories and the quantum de Finetti theorem
Tobias Fritz, Antonio Lorenzin
Markov categories have recently emerged as a powerful high-level framework for probability theory and theoretical statistics. Here we study a quantum version of this concept, calle…
Approaching the Continuous from the Discrete: an Infinite Tensor Product Construction
Antonio Lorenzin, Fabio Zanasi
Increasingly in recent years, probabilistic computation has been investigated through the lenses of categorical algebra, especially via string diagrammatic calculi. Whereas categor…
Absolute continuity, supports and idempotent splitting in categorical probability
Tobias Fritz, Tomáš Gonda, Antonio Lorenzin +2
Markov categories have recently turned out to be a powerful high-level framework for probability and statistics. They accommodate purely categorical definitions of notions like con…
Empirical Measures and Strong Laws of Large Numbers in Categorical Probability
Tobias Fritz, Tomáš Gonda, Antonio Lorenzin +2
The Glivenko--Cantelli theorem is a uniform version of the strong law of large numbers. It states that for every IID sequence of random variables, the empirical measure converges t…
Categories of abstract and noncommutative measurable spaces
Tobias Fritz, Antonio Lorenzin
Gelfand duality is a fundamental result that justifies thinking of general unital -algebras as noncommutative versions of compact Hausdorff spaces. Inspired by this perspectiv…
Bayesian Networks, Markov Networks, Moralisation, Triangulation: a Categorical Perspective
Antonio Lorenzin, Fabio Zanasi
Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to…