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Stream: theory: categorical probability

Topic: "Bernoulli-based" distributive Markov categories

Sam Staton (Nov 03 2023 at 21:12):

Hi, We have recently come to look at a notion of "Bernoulli-based distributive Markov category". This is a Markov category $C$ with coproducts and a faithful distributive Markov functor $C_\mathbb{N}\to \mathbf{FinStoch}$, where $C_{\mathbb{N}}$ comprises the numerals $1+..+1$. The idea is that we can have all kinds of spaces and crazy kernels in $C$, but on the numerals, it should be the familiar Bernoulli probability of $\mathbf{FinStoch}$.

Does it connect to other ideas?

Sam Staton (Nov 03 2023 at 21:14):

We used these in this paper (accepted at the POPL conference, conditionally). We have some methods for building them. From the perspective of categorical probability, the paper is about a correspondence between Markov categories of a certain kind and graphons. (We've been at it for a while, and I mentioned some preliminary results at the CPS workshop in 2020.)