MACHINE LEARNING

Bayesian machine learning via category theory

Resource type
Authors/contributors
Title
Bayesian machine learning via category theory
Abstract
From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning. Using categorical methods, we construct models for parametric and nonparametric Bayesian reasoning on function spaces, thus providing a basis for the supervised learning problem. In particular, stochastic processes are arrows to these function spaces which serve as prior probabilities. The resulting inference maps can often be analytically constructed in this symmetric monoidal weakly closed category. We also show how to view general stochastic processes using functor categories and demonstrate the Kalman filter as an archetype for the hidden Markov model.
Publication
arXiv:1312.1445 [math]
Date
2013-12-05
Accessed
2019-11-22T17:32:35Z
Library Catalog
Extra
ZSCC: 0000006 arXiv: 1312.1445
Notes
Comment: 74 pages, comments welcome
Citation
Culbertson, J., & Sturtz, K. (2013). Bayesian machine learning via category theory. ArXiv:1312.1445 [Math]. Retrieved from http://arxiv.org/abs/1312.1445
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