Dan Shiebler - Categorical Stochastic Processes and Likelihood

compositionality:13511 - Compositionality, April 14, 2021, Volume 3 (2021) - https://doi.org/10.32408/compositionality-3-1
Categorical Stochastic Processes and LikelihoodArticle

Authors: Dan Shiebler 1

  • 1 Department for Continuing Education and Department of Computer Science, University of Oxford, Oxford, United Kingdom

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Volume: Volume 3 (2021)
Published on: April 14, 2021
Imported on: May 2, 2024
Keywords: Computer Science - Artificial Intelligence,Mathematics - Category Theory

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