The Chair for the Methods of Machine Learning studies Algorithms for and as learning machines.
Numerical Problems --- linear algebra and optimization, integration and the solution of differential equations --- are the computational bottleneck of artificial intelligent systems. Intriguingly, the numerical algorithms used for these tasks are also compact little intelligent agents themselves. They estimate unknown / uncomputable quantities by observing the result of feasible computations. They also actively decide which computations to perform.
We study this philosophical and mathematical connection between computation and inference, aiming to build a theoretical understanding of numerical computer algorithms as agents acting rationally under uncertainty. We analyse existing algorithms from this viewpoint, and propose novel algorithms that provide functionality for key computational challenges in machine learning. Uncertaintyplays a key role in this analysis. From this perspective, and with the help of international collaborators, we have helped establish the concept of probabilistic numerics. The first textbook on the subject was published in 2022 by Cambridge University Press.
