Seminar Announcement
Date: Thursday, 27 February 2025
Time: 10:30 AM
Venue: Seminar Hall
Bayesian filtering and Smoothing in Markov categories
Areeb Mohammed Shah
University of Innsbruck, Austria.
27-02-25

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Abstract

Markov categories are an actively growing framework for probabilistic reasoning. Markov categories can be used to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of conditional independences and algorithms for Bayesian filtering and smoothing applicable in all Markov categories with conditionals.

When instantiated in appropriate Markov categories, these algorithms specialize to existing ones such as the Kalman filter, forward-backward algorithm, and the Rauch–Tung–Striebel smoother. The generality of this framework allows for a unified account of hidden Markov models and associated algorithms in discrete probability, Gaussian probability, measure-theoretic probability, “possibilistic” nondeterminism, and others simultaneously. Additionally, the string diagram calculus associated to a Markov category provides an intuitive visual representation of the underlying information flow.