Periodic Reporting for period 2 - BLaSt (Better Languages for Statistics: foundations for non-parametric probabilistic programming)
Reporting period: 2022-04-01 to 2023-09-30
Probabilistic programming is a powerful method for Bayesian statistical modelling, particularly where the sample space is complex or unbounded (non-parametric). This is because the statistical model can be described clearly in a way that is precise but separate from inference algorithms. It accommodates complex models in such a way that outcomes are still explainable.
The objective of the proposed research is to develop a semantic foundation for probabilistic programming that properly explains the non-parametric aspects, particularly the symmetries that arise there. There are three ultimate goals:
■ to propose new probabilistic programming languages: better languages for statistics;
■ to devise new general inference methods for probabilistic programs;
■ to build new foundations for probability.
The objective of the proposed research is to develop a semantic foundation for probabilistic programming that properly explains the non-parametric aspects, particularly the symmetries that arise there. There are three ultimate goals:
■ to propose new probabilistic programming languages: better languages for statistics;
■ to devise new general inference methods for probabilistic programs;
■ to build new foundations for probability.
The work so far has proposed new semantic foundations for programming languages and probabilistic programs, based on categories of concrete sheaves, monads, and Markov categories.
New results in probability theory have also been achieved: new theorems about hierarchical exchangeability, and new treatments of the quantum analogue of de Finetti's theorem.
We have developed new foundations for gradient methods in probabilistic programming.
We have also developed a new programming library for probabilistic programming, based on the techniques developed.
New results in probability theory have also been achieved: new theorems about hierarchical exchangeability, and new treatments of the quantum analogue of de Finetti's theorem.
We have developed new foundations for gradient methods in probabilistic programming.
We have also developed a new programming library for probabilistic programming, based on the techniques developed.
For the remainder of the project we will derive new methods in programming languages so as to advance the state of the art in statistics and probability theory.
We hope to prove a conjecture precisely relating programming libraries to "exchangeable process" in non-parametric statistics.
We will further develop our probabilistic programming library based on further developments. We hope to extend it with gradient methods for advanced performance.
We hope to prove a conjecture precisely relating programming libraries to "exchangeable process" in non-parametric statistics.
We will further develop our probabilistic programming library based on further developments. We hope to extend it with gradient methods for advanced performance.