3 citations · 3 across the 2 of their papers we have counts for
8 papers
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…
Convergence of martingales via enriched dagger categories
Paolo Perrone, Ruben Van Belle
We provide a categorical proof of convergence for martingales and backward martingales in mean, using enriched category theory. The enrichment we use is in topological spaces, with…
Dilations and information flow axioms in categorical probability
Tobias Fritz, Tomáš Gonda, Nicholas Gauguin Houghton-Larsen +3
We study the positivity and causality axioms for Markov categories as properties of dilations and information flow in Markov categories, and in variations thereof for arbitrary sem…
Categorical probability spaces, ergodic decompositions, and transitions to equilibrium
Noé Ensarguet, Paolo Perrone
We study a category of probability spaces and measure-preserving Markov kernels up to almost sure equality. This category contains, among its isomorphisms, mod-zero isomorphisms of…
Lifting couplings in Wasserstein spaces
Paolo Perrone
This paper makes mathematically precise the idea that conditional probabilities are analogous to path liftings in geometry. The idea of lifting is modelled in terms of the category…