Probabilistic Linear Solvers - Treating Approximation as Inference

Linear equation systems (Ax=b) are at the core of many, more sophisticated numerical tasks. However, for large systems (e.g. least-squares problems in Machine Learning) it becomes necessary resort to approximation. Typical approximation algorithms for linear equation systems tend to return only a point estimate of the solution but little information about its quality (maybe a residual or a worst-case error bound). Probabilistic linear solvers aim to provide more information in form of a probability distribution over the solution. This talk will show how to design efficient probabilistic linear solvers, how they are connected to classic solvers and how preconditioning can be seen from an inference perspective.