Data-efficient and safe learning with Gaussian processes

Abstract

Data-based modeling techniques enjoy increasing popularity in many areas of science and technology where traditional approaches are limited regarding accuracy and efficiency. When employing machine learning methods to generate models of dynamic system, it is necessary to consider two important issues. Firstly, the data-sampling process should induce an informative and representative set of points to enable high generalization accuracy of the learned models. Secondly, the algorithmic part for efficient model building is essential for applicability, usability, and the quality of the learned predictive model. This thesis deals with both of these aspects for supervised learning problems, where the interaction between them is exploited to realize an exact and powerful modeling. After introducing the non-parametric Bayesian modeling approach with Gaussian processes and basics for transient modeling tasks in the next chapter, we dedicate ourselves to extensions of this probabilistic technique to relevant practical requirements in the subsequent chapter. This chapter provides an overview on existing sparse Gaussian process approximations and propose some novel work to increase efficiency and model selection on particularly large training data sets. For example, our sparse modeling approach enables real-time capable prediction performance and efficient learning with low memory requirements. A comprehensive comparison on various real-world problems confirms the proposed contributions and shows a variety of modeling tasks, where approximate Gaussian processes can be successfully applied. Further experiments provide more insight about the whole learning process, and thus a profound understanding of the presented work. In the fourth chapter, we focus on active learning schemes for safe and information-optimal generation of meaningful data sets. In addition to the exploration behavior of the active learner, the safety issue is considered in our work, since interacting with real systems should not result in damages or even completely destroy it. Here we propose a new model-based active learning framework to solve both tasks simultaneously. As basis for the data-sampling process we employ the presented Gaussian process techniques. Furthermore, we distinguish between static and transient experimental design strategies. Both problems are separately considered in this chapter. Nevertheless, the requirements for each active learning problem are the same. This subdivision into a static and transient setting allows a more problem-specific perspective on the two cases, and thus enables the creation of specially adapted active learning algorithms. Our novel approaches are then investigated for different applications, where a favorable trade-off between safety and exploration is always realized. Theoretical results maintain these evaluations and provide respectable knowledge about the derived model-based active learning schemes. For example, an upper bound for the probability of failure of the presented active learning methods is derived under reasonable assumptions. Finally, the thesis concludes with a summary of the investigated machine learning problems and motivate some future research directions.