Foundations for Type-Driven Probabilistic Modelling with Quasi-Borel Spaces

Function-spaces and other abstract types enable modular and flexible programming style with reusable building blocks. If we try to use the same abstractions for probabilistic modelling, we encounter hard no-go results which require traditional approaches to use non-standard abstractions. In this talk, I will describe a simple algebraic structure---the quasi-Borel space---that supports expressive type-structure, including function spaces and type-dependency. I will review their basic definitions and properties. Time permitting, I will outline recent results and directions.