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Stream: event: ACT20

Topic: July 6: Tobias Fritz et al.'s talk

Paolo Perrone (Jul 02 2020 at 02:37):

Hello all! This is the thread of discussion for the talk of Tobias Fritz, Tomáš Gonda, Paolo Perrone and Eigil Rischel, "Distribution functors, second-order stochastic dominance and the Blackwell-Sherman-Stein Theorem in Categorical Probability".
Date and time: Monday July 6, 16:00 UTC.
Zoom meeting: https://mit.zoom.us/j/7055345747
YouTube live stream: https://www.youtube.com/watch?v=1WhsWK20iRo&list=PLCOXjXDLt3pZDHGYOIqtg1m1lLOURjl1Q

Paolo Perrone (Jul 03 2020 at 14:40):

For more background on Markov categories, probability monads, and categorical probability in general, this is the playlist you are looking for: https://www.youtube.com/playlist?list=PLaILTSnVfqtIebAXFOcee9MvAyBwhIMyr

Tomáš Gonda (Jul 03 2020 at 15:03):

In this talk, I will be speaking about a project tentatively titled:

Distribution functors, second-order stochastic dominance and the Blackwell--Sherman--Stein Theorem in Categorical Probability

It is a work in collaboration with Tobias Fritz, Paolo Perrone, and Eigil Rischel; in which we study what can one do with Markov categories that have distribution objects, which one can think of as spaces of measures. With this kind of structure, we can prove abstract versions of results such as:

The equivalence between the existence of partial evaluations between two measures and the second-order stochastic dominance relation of the two measures. The latter is a common way to compare measures in terms of how "spread out" they are and the former is the lowest level of the bar construction.
Blackwell-Sherman-Stein Theorem. This result characterizes the "informativeness" order relation of statistical models defined in terms of the existence of a simulation of one from the other. In particular, it shows that this relation is isomorphic to the second-order stochastic dominance relation of measures over the space of posterior distributions over the tested hypotheses that a Bayesian agent would assign having performed the statistical experiment. That is, a statistical experiment is more informative iff the posteriors are more spread out (so that doing the experiment allows one to distinguish between the hypotheses better), in a precise sense that we can now make use of in any suitable Markov category.

Apart from generalizing some known results from mathematical statistics, we also advance the theoretical understanding of Markov categories relevant to these concepts. Specifically, we elucidate the relation between Markov categories and monoidal monads - showing under what conditions can we think of a Markov category as the Kleisli category of a probability monad (and vice versa).

blackwell_act.pdf

Tomáš Gonda (Jul 03 2020 at 15:08):

And to complement Paolo's link to the talks from a recent conference on categorical probability, here's a nice playlist of introductory videos on the topic by @Arthur Parzygnat.

Arthur Parzygnat (Jul 03 2020 at 20:06):

Thanks for subscribing me, @Tomáš Gonda! This looks really cool!

Tomáš Gonda (Jul 06 2020 at 14:45):

Here are my slides for the presentation :slight_smile:

Paolo Perrone (Jul 06 2020 at 15:55):

We start in 5 minutes!

Paolo Perrone (Jul 06 2020 at 16:40):

The paper by Cho and Jacobs: https://arxiv.org/abs/1709.00322

Paolo Perrone (Jul 07 2020 at 01:21):

Here's the video!
https://www.youtube.com/watch?v=fgWUV-hE0CI&list=PLCOXjXDLt3pYot9VNdLlZqGajHyZUywdI

Paolo Perrone (Jul 07 2020 at 12:09):

By the way, for the people interested in probability and statistics, you may want to take a look at the stream of the categorical probability conference.

Paolo Perrone (Jul 07 2020 at 12:09):

We also have a dedicated Jitsi room,
Probability - random topics are welcome and encouraged.

Paolo Perrone (Jul 14 2020 at 19:47):

Hello! If anyone is interested, this week Tobias Fritz will give a talk about Markov categories at the MIT Categories Seminar.
Thread here: https://categorytheory.zulipchat.com/#narrow/stream/229457-MIT-Categories.20Seminar/topic/July.2016.3A.20Tobias.20Fritz'.20talk

Tomáš Gonda (Oct 16 2020 at 02:24):

This project is now on arXiv with quite a bit of new content added since July: https://arxiv.org/abs/2010.07416

Paolo Perrone (Nov 17 2020 at 14:37):

Hello all! There's a talk on Markov category here, this week: https://categorytheory.zulipchat.com/#narrow/stream/229457-MIT-Categories.20Seminar/topic/November.2019.3A.20Eigil.20Rischel's.20talk