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Will Jump (Oct 27 2025 at 22:25):Hello all,
I was having a look through n-lab and found a post advertising a reading group for category theory in statistics from 2020 (https://golem.ph.utexas.edu/category/2020/06/statistics_for_category_theori.html) along with a great shortlist of papers. Does this group or one like it still exist? It'd be great to have some more reading recommendations particularly around categories applied to statistics (I'm particularly interested in dempster schafer theory at the moment) and stuff on the edge between categories, probability and topology (like information geometry or locale probability).
Cheers! - Will
Paolo Perrone (Oct 28 2025 at 09:46):Hello. I don't think that group exists anymore.
For people applying category theory to statistics, I'm aware of Rob Cornish (Markov categories and neural networks) and Pedro Terán (possibility theory using categories).
Some theoretical results can be found in the work of Fritz et al., e.g. here, here, the last three sections here, and here.
For papers, you might have seen this list on the nLab.
Information geometry and its links with category theory are still quite new subjects. Myself, I've worked a little bit on both, see for example this paper and this talk.
There is also the work of Hong Van Le et al., see for example here and follow the references in there.
For locales, it's usually some form of measure theory rather than probability, as for example in this recent preprint.
Not quite about locales, but similar in 'point-free' spirit, there are also algebraic and order-theoretic approaches to probability and measure theory, for example in the work of Fritz, Lorenzin, Moss and others - start here and here.
(There are for sure a lot of other people, papers, etc. - This is what I can think of right now, someone might want to add some.)
Paolo Perrone (Oct 28 2025 at 09:49):By the way, while that group is not active, there is a channel on this Zulip specifically for categorical probability and statistics, make sure you subscribe to it!
Will Jump (Oct 28 2025 at 18:09):Thanks Paolo, I'm now on the channel!