28 citations · 159 across the 26 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…
De Finetti's Theorem in Categorical Probability
Tobias Fritz, Tomáš Gonda, Paolo Perrone
We present a novel proof of de Finetti's Theorem characterizing permutation-invariant probability measures of infinite sequences of variables, so-called exchangeable measures. The…
Stochastic order on metric spaces and the ordered Kantorovich monad
Tobias Fritz, Paolo Perrone
In earlier work, we had introduced the Kantorovich probability monad on complete metric spaces, extending a construction due to van Breugel. Here we extend the Kantorovich monad fu…
Bimonoidal Structure of Probability Monads
Tobias Fritz, Paolo Perrone
We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability mo…
A Probability Monad as the Colimit of Spaces of Finite Samples
Tobias Fritz, Paolo Perrone
We define and study a probability monad on the category of complete metric spaces and short maps. It assigns to each space the space of Radon probability measures on it with finite…