TY - JOUR
TI - A Convenient Category for Higher-Order Probability Theory
AU - Heunen, Chris
AU - Kammar, Ohad
AU - Staton, Sam
AU - Yang, Hongseok
T2 - arXiv:1701.02547 [cs, math]
AB - Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.
DA - 2017/01/10/
PY - 2017
DP - arXiv.org
UR - http://arxiv.org/abs/1701.02547
Y2 - 2019/10/10/11:48:09
ER -