Better Languages for Statistics: foundations for non-parametric probabilistic programming

Project Information

BLaSt

Grant agreement ID: 864202

DOI

10.3030/864202

EC signature date 26 February 2020

Start date 1 October 2020

End date 30 September 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 931 178,00

EU contribution

€ 1 931 178,00

Coordinated by

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom

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

Summary of the context and overall objectives of the project

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.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

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.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

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.

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