With international collaborators, we have developed and continue to expand the paradigm of probabilistic numerics that describes computation itself as an inference process. On the algorithmic level, machine learning requires challenging numerical computations. But these numerical computations themselves are also instances of inference problems. Numerical algorithms — methods for optimization, integration, linear algebra, etc. — can thus be described and analysed as autonomous learning agents. Among the advantages of this description is that it makes computational uncertainty a first-class citizen. This is important because big-data computation is typically extremely imprecise and stochastic.

Our group has developed several software packages that provide novel functionality for efficient and reliable machine learning. Although the software stack of machine learning and data analysis has improved rapidly and drastically in recent years, many methodological challenges remain. The computational toolchain has to simultaneously become easier to use and increasingly flexible. And it has to drastically reduce the use of computational resources for learning and inference. With our software development we aim to add avant-garde functionality to the toolbox of ML researchers. In some cases our work has found its way into larger, third-party open source software packages for general consumption by ML engineers.