2013/12/05 by Jared Culbertson, Culbertson, Jared, Kirk Sturtz +1 · 14 citations
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Bayesian probability #Categorical variable #Category Theory (math.CT) #Category theory #Computer science #FOS: Mathematics #Machine learning #Mathematics #Pure mathematics #Statistical Mechanics and Entropy #Theoretical computer science #math.CT
paper · pdf · doi:10.48550/arxiv.1312.1445
published in arXiv (Cornell University) (Cornell University) · 74 pages, comments welcome
arxiv created 2013/12/05 · openalex publication_date 2013/12/05 · arxiv updated 2013/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.