TY - JOUR
TI - Bayesian machine learning via category theory
AU - Culbertson, Jared
AU - Sturtz, Kirk
T2 - arXiv:1312.1445 [math]
AB - 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.
DA - 2013/12/05/
PY - 2013
DP - arXiv.org
UR - http://arxiv.org/abs/1312.1445
Y2 - 2019/11/22/17:32:35
KW - Bayesianism
KW - Categorical ML
KW - Categorical probability theory
KW - Purely theoretical
ER -