Probabilistic Numerical Methods - From Theory to Implementation

Motivation

Numerical methods provide the computational foundation of science and power automated data analysis and inference in its contemporary form of machine learning. Probabilistic numerical methods aim to explicitly represent uncertainty resulting from limited computational resources and imprecise inputs in these models. In recent years, algorithms arising from this formalism have repeatedly shown that they can enrich and improve upon classic methods in tasks where hyperparameter adaptation is not straightforward; where computational stochasticity and low precision play a prominent role; where limited data make uncertainty quantification a key functionality; where related problems have to be solved repeatedly; and where extreme scale or tight budgets call for rough approximations at low cost.

With theoretical analysis well underway, software development is now a key next step to wide-spread success.

From Lapack to SciPy to PyTorch, open-source software libraries have driven scientific advancement in their respective domains. Indeed, the lack of high-quality implementations of probabilistic numerical methods is increasingly a bottleneck for our field. Addressing this issue is a main goal of the seminar. We recently started a community effort to develop an open-source framework named ProbNum. You can track its progress at https://probnum.readthedocs.io/.

The goals of this Dagstuhl Seminar are thus two-fold. First, we want to rekindle our community spirit. The meeting will provide the opportunity to update others on your own research and to discuss new directions and ideas together, after the deadening silence of the Covid years. We have invited a diverse group of people like yourself, hailing from CS/AI/ML, from statistics, optimization, and from numerical analysis. On the other hand, the seminar will act as a milestone for the ProbNum software: we hope some of you may want to join the development effort to shape functionality, structure and interface of the library ahead of a first release, and an associated publication.

Hybrid Format

Exceptional times require exceptional measures. Dagstuhl seminars have always been about bringing people together in person, in a deliberately remote place. This year, however, some of this interaction will have to take place remotely , after all: All scientific talks of the seminar will be streamed online and even the speakers will not all be present at the castle (a silver lining is that we can increase the number of online participants if necessary). But the last year has also shown painfully that some forms of collaboration do not work without close personal interaction. We thus ask you to decide for yourself: If you are primarily interested in attending the scientific talks – or in giving one of them – we understand if you prefer to attend virtually. The talks will take up only limited hours of the day, typically in the afternoon, local time. If you want to be directly involved in small-group discussions, also after hours, and particularly in the software development effort, we hope you will choose to attend in person. This is, of course, assuming that the course of the pandemic will allow us, legally and practically, to actually meet at the castle in late October. Please let us and Dagstuhl admin know as early as possible if you plan to participate virtually, as this will allow us to invite further people from our waiting list to the castle itself.