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Stream: event: Online CT seminar

Topic: July 3 1400 GMT - Paolo Perrone - Markov Categories

Eric M Downes (Jun 29 2024 at 14:46):

From Paolo:

"""
Title:
Markov categories, Bayesian inversions, and statistical experiments

Abstract:
Markov categories are one of the most recent abstract frameworks for probability, statistics, and related fields.
They can be considered a higher abstraction layer on top of measure theory, where one can work with concepts such as disintegrations and regular conditionals without using measure theory directly.
In the past few years they have been successfully employed to restate, reprove, and even generalize core concepts of probability theory, from de Finetti's theorem to d-separation criteria, only using diagrammatic manipulations.
In this talk I will explain the main theory of Markov categories and their relationship with monads, with particular emphasis on conditioning and Bayesian inversions.
Given time and interest, I can also show how to apply these ideas to statistical experiments, and extend Blackwell's theorem, for the first time, beyond the discrete case.

Relevant papers:

P. Perrone, "Markov Categories and Entropy", IEEE Transactions of Information Theory 70(3), 2024. (arXiv:2212.11719)
T. Fritz, T. Gonda, P. Perrone and E. F. Rischel, "Representable Markov categories and comparison of statistical experiments in categorical probability", Theoretical Computer Science 961, 2023. (arXiv:2010.07416)
N. Ensarguet and P. Perrone, "Categorical probability spaces, ergodic decompositions, and transitions to equilibrium", submitted. (arXiv:2310.04257)
"""