Paolo Perrone

A categorical account of the Metropolis-Hastings algorithm Metropolis-Hastings (MH) is a foundational Markov chain Monte Carlo (MCMC) algorithm. In this paper, we ask whether it is possible to formulate and analyse MH in terms of categorical probability, usin...

Metropolis-Hastings using Markov categories!
A work by Rob Cornish and Andi Wang.
arxiv.org/abs/2601.22911

Bayesian Networks, Markov Networks, Moralisation, Triangulation: a Categorical Perspective Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian netw...

More on the relationship between string diagrams and probabilistic graphical models.
New work by Antonio Lorenzin and Fabio Zanasi.
arxiv.org/abs/2512.09908

Compositional Inference for Bayesian Networks and Causality Inference is a fundamental reasoning technique in probability theory. When applied to a large joint distribution, it involves updating with evidence (conditioning) in one or more components (variables...

New work by Bart Jacobs, Márk Széles and Dario Stein.
arxiv.org/abs/2512.00209

YouTube video by Topos Institute [Oxford Seminar] Paolo Perrone | Descent in Probability Theory: the first steps downward

Descent in Probability Theory: the first steps down
youtu.be/VG2RTE1R0BY?...

Anyone in Milan tomorrow?

YouTube video by Paolo Perrone Paolo Perrone - Independent States Are Orthogonal - GSI 2025

"Independent States Are Orthogonal", a talk at GSI 2025 bridging probability and geometry.
youtu.be/mUPJEt3FeiU

TOMAS GONDA: Introduction to Categorical Probability YouTube video by IQOQI Vienna

New introduction to Categorical Probability for Physicists, by Tomáš Gonda:
www.youtube.com/live/eVfFuIG...

Partializations of Markov categories The present work develops a construction of a CD category of partial kernels from a particular type of Markov category called a partializable Markov category. These are a generalization of earlier mod...

Great work by Areeb Shah-Mohammed on partial morphisms in Markov categories.
arxiv.org/abs/2509.05094

We should call it 'connecting the DOTS'.

YouTube video by Paolo Perrone Categories of relations which compose independently - Paolo Perrone

A categorical definition of independence!
Here is a recording of the talk I gave at CT 2025, for anyone who might have missed it.
youtu.be/ls6zOX8L1eI

Dagger categories of relations: the equivalence of dilatory dagger categories and epi-regular independence categories Several categories look like categories of relations, but do not fit the established theory of relations in regular categories. They include the category of surjective multivalued functions, the categ...

New paper out!
arxiv.org/abs/2508.01146

The document that started categorical probability, part of secret work from 1962, has reappeared, together with new commentaries of its author, Bill Lawvere.
lawverearchives.com/wp-content/u...
Thanks to Tobias Fritz and to the Lawvere Archives for the work.

It seems that it's the year of double categories.

I'm excited to be in Bologna for the week!
(If anyone is here and wants to meet, write me an email.)

Me, every time the EU "wants to attract researchers":

We start in 10 minutes!

Categories of abstract and noncommutative measurable spaces Gelfand duality is a fundamental result that justifies thinking of general unital $C^*$-algebras as noncommutative versions of compact Hausdorff spaces. Inspired by this perspective, we investigate wh...

What are point-free measurable spaces, and what is their quantum equivalent?
Great work by Tobias Fritz and Antonio Lorenzin.
arxiv.org/abs/2504.13708

Empirical Measures and Strong Laws of Large Numbers in Categorical Probability 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 to the underlying dist...

We finally have the strong law of large numbers in Markov categories.
arxiv.org/abs/2503.21576

Electric Dreams | Tate Modern

To all my UK-based mutual are into 'cybernetics', I very strongly recommend this exhibition in London.
www.tate.org.uk/whats-on/tat...

Random Variables, Conditional Independence and Categories of Abstract Sample Spaces Two high-level "pictures" of probability theory have emerged: one that takes as central the notion of random variable, and one that focuses on distributions and probability channels (Markov kernels). ...

New great work by Dario Stein.
arxiv.org/abs/2503.02477

Categorical algebra of conditional probability In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this p...

What do Beck-Chevalley monads have to do with conditional probability?
arxiv.org/abs/2502.14941

Wait, espresso doesn't make you think about math?

If there was anybody competent in charge in Europe we would be passing emergency legislation this week so that starting next week we poach every scientist from the US who was previously funded by NSF, NIH etc. Oh well, we can dream.

GitHub - alex404/goal: The Geometric OptimizAtion Libraries The Geometric OptimizAtion Libraries. Contribute to alex404/goal development by creating an account on GitHub.

Never forget that you do can do natural gradient descent in Haskell!
github.com/alex404/goal

Using "many" for something that's counted by a natural number and "much" for something that's counted by a real number (and a unit, usually) is actually a good approximation.

Excited to be in Seattle for the JMM!
Besides ACT today and categorical probability on Saturday, which sessions are my fellow category theorists attending?

(Reposting)
One thing that we don't stress enough is that the correspondence morphisms-programs is true also *outside* the cartesian closed (=functional) case.
Morphisms are programs, regardless of whether they form their own object/type or not.

I don't know if this models all the examples you have in mind, but in every monoidal category, the monoidal unit is canonically a monoid.

Lyckönskningar!

Yes. (Or at least a decategorification thereof.)