Machine learning seeks to automatize the processing oflarge complex datasets by adaptive computing, a core strategy to meet growingdemands of science and applications.Typically, real-world problems are mapped to penalized estimation tasks (e.g.,binary classification), which are solved by simple efficient algorithms. Whilesuccessful so far, I believe this approach is too limited torealise the potential of adaptive computing. Most of the work, such as dataselection, feature construction, model calibration and comparison, still has tobe done by hand. Demands for automated decision-making (e.g., tuningdata acquisition during an experiment) are not met.Such problems are naturally addressed by Bayesian reasoning about uncertainknowledge, which however remains infeasible in most large scale settings.The main goal of this proposal is to unite the strengths of penalizedestimation and Bayesian decision-making, exploiting the former's advanced stateof the art in order to implement substantial improvements coming withthe latter in large scale applications. A major focus is on improving magneticresonance imaging (MRI) by way of new Bayesian technology, driving robustnonlinearreconstruction from less data, and optimizing the acquisition throughBayesian experimental design, applications not previously attempted by machinelearning. Far beyond the reach of present methodology, these goals demanda novel computational foundation for approximate Bayesian inference throughnumerical algorithmic reductions.This project will have high impact on probabilistic machine learning, raisingthe bar for scalable Bayesian computations. It will help to open up a whole newrange of medical imaging applications for machine learning. Moreover,substantial impact on MRI reconstruction research is anticipated. There isstrong recent interest in savings through compressive sensing, whose fullpotential is realised only by way of adaptive technology such as projectedhere.