11 citations · 17 across the 11 of their papers we have counts for
11 papers
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…
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…
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…
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…
An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models
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…
The Aldous$\unicode{x2013}$Hoover Theorem in Categorical Probability
Leihao Chen, Tobias Fritz, Tomáš Gonda +2
The Aldous-Hoover Theorem concerns an infinite matrix of random variables whose distribution is invariant under finite permutations of rows and columns. It states that, up to equal…
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…
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…
Formality and strongly unique enhancements
Antonio Lorenzin
Inspired by the intrinsic formality of graded algebras, we prove a necessary and sufficient condition for strongly uniqueness of DG-enhancements. This approach offers a generalizat…
Compatibility of t-structures in a semiorthogonal decomposition
Antonio Lorenzin
We describe how to obtain a global t-structure from a semiorthogonal decomposition with compatible t-structures on every component. This result is used to generalize a well-known t…
A comparative analysis of standard accretion disks spectra: an application to Ultraluminous X-ray Sources
A. Lorenzin, L. Zampieri
We compare standard models of accretion disks around black holes that include the appropriate zero-torque inner boundary condition and relativistic effects on the emission and prop…