Probabilistic machine learning for pattern recognition and design exploration

The following thesis deals with the development of new probabilistic machine learning models with a focus on efficiency, flexibility, applicability, scalability and high prediction accuracy. Therefore, learning tasks from the areas of regression, classification, image classification, time series as well as the representation of spatial and / or temporally correlated quantities are examined. In order to achieve these goals and in addition to the development of the models themselves, their interaction to the field of data generation is also investigated. The calculable uncertainty of the probabilistic models is used to obtain the maximum information gain with as few data points as possible. This methodology is also used for the efficient solving of optimization problems. Besides obtaining an accurate approximation model of the data, a deeper understanding of the correlations between input and output is desired, therefore the topic of sensitivity analysis is a further part of this work. The developed probabilistic models are used to evaluate the number of calculations needed to estimate the sensitivities as efficiently as possible, even for correlated inputs