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

Informations projet

BLaSt

N° de convention de subvention: 864202

DOI

10.3030/864202

Date de signature de la CE 26 Février 2020

Date de début 1 Octobre 2020

Date de fin 30 Septembre 2026

Financé au titre de

• EXCELLENT SCIENCE - European Research Council (ERC)

Coût total

€ 1 931 178,00

Contribution de l’UE

€ 1 931 178,00

Coordonné par

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)

Période du rapport: 2022-04-01 au 2023-09-30

Résumé du contexte et des objectifs généraux du projet

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.

Travail effectué depuis le début du projet jusqu’à la fin de la période considérée dans le rapport et principaux résultats atteints jusqu’à présent

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.

Progrès au-delà de l’état des connaissances et impact potentiel prévu (y compris l’impact socio-économique et les conséquences sociétales plus larges du projet jusqu’à présent)

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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