ABSTRACT
We take a category-theoretic perspective on the relationship between probabilistic modeling and gradient based optimization. We define two extensions of function composition to stochastic process subordination: one based on a co-Kleisli category and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category of Markov kernels $\mathbf{Stoch}$ through a pushforward procedure.
We extend stochastic processes to parametric statistical models and define a way to compose the likelihood functions of these models. We demonstrate how the maximum likelihood estimation procedure defines a family of identity-on-objects functors from categories of statistical models to the category of supervised learning algorithms $\mathbf{Learn}$.
Code to accompany this paper can be found on GitHub (https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood).
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► References
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Cited by
[1] Geoffrey S. H. Cruttwell, Bruno Gavranović, Neil Ghani, Paul Wilson, and Fabio Zanasi, Lecture Notes in Computer Science 13240, 1 (2022) ISBN:978-3-030-99335-1.
[2] Georgios Bakirtzis and Ufuk Topcu, 2022 ACM/IEEE 13th International Conference on Cyber-Physical Systems (ICCPS) 308 (2022) ISBN:978-1-6654-0967-4.
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