Paper Published! | Areeb SM's website

Well, the preprint we¹ wrapped up last year on hidden Markov models and Bayesian filtering is finally published (Fritz et al., 2025).

It’s been a long time coming, but I guess that’s just how it goes sometimes. It’s more or less the same as the arXiv version, but the arXiv version isn’t in the journal format (it also seems to have processed the string diagrams differently). That said, at least my name shows up right this time :D

I’ve made sure my name is “Shah Mohammed” in all the later arXiv preprints, but that seems to have come at the cost of my first name being parsed as “Areeb Shah”. Should probably figure out how to fix that :/

Tobias Fritz, Andreas Klingler, Drew McNeely, Yuwen Wang and I. ↩

References

Hidden Markov Models and the Bayes Filter in Categorical Probability

Tobias Fritz, Andreas Klingler, Drew McNeely, Areeb Shah Mohammed, and Yuwen Wang

IEEE Transactions on Information Theory, Sep 2025

Abs DOI arXiv Code

We use Markov categories 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. We also prove that the sequence of outputs of our abstract Bayes filter is itself a Markov chain with a concrete formula for its transition maps. There are two main features of this categorical framework. The first is its abstract generality, as manifested in our unified account of hidden Markov models and algorithms for filtering and smoothing in discrete probability, Gaussian probability, measure-theoretic probability, possibilistic nondeterminism and others at the same time. The second feature is the intuitive visual representation of information flow in terms of string diagrams.

References

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