We propose a new active learning algorithm for parametric linear regression with random design. We provide finite sample convergence guarantees for general distributions in the misspecified model. This is the first active learner for this setting that provably can improve over passive learning. Unlike other learning settings (such as classification), in regression the passive learning rate of O(1/epsilon) cannot in general be improved upon. Nonetheless, the so-called `constant' in the rate of convergence, which is characterized by a distribution-dependent risk, can be improved in many cases. For a given distribution, achieving the optimal risk requires prior knowledge of the distribution. Following the stratification technique advocated in Monte-Carlo function integration, our active learner approaches a the optimal risk using piecewise constant approximations.

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Our domain transfer network can translate between fixed representations without having to learn or finetune them.

Time series data, defined by equally spaced points over time, is essential in fields like medicine, telecommunications, and energy. Analyzing it involves tasks such as classification, clustering, prototyping, and regression. Classification identifies normal vs. abnormal movements in skeleton-based motion sequences, clustering detects stock market behavior patterns, prototyping expands physical therapy datasets, and regression predicts patient recovery. Deep learning has recently gained traction in time series analysis due to its success in other domains. This thesis leverages deep learning to enhance classification with feature engineering, introduce foundation models, and develop a compact yet state-of-the-art architecture. We also address limited labeled data with self-supervised learning. Our contributions apply to real-world tasks, including human motion analysis for action recognition and rehabilitation. We introduce a generative model for human motion data, valuable for cinematic production and gaming. For prototyping, we propose a shape-based synthetic sample generation method to support regression models when data is scarce. Lastly, we critically evaluate discriminative and generative models, identifying limitations in current methodologies and advocating for a robust, standardized evaluation framework. Our experiments on public datasets provide novel insights and methodologies, advancing time series analysis with practical applications.

Within one decade, Deep Learning overtook the dominating solution methods of countless problems of artificial intelligence. ``Deep'' refers to the deep architectures with operations in manifolds of which there are no immediate observations. For these deep architectures some kind of structure is pre-defined -- but what is this structure? With a formal definition for structures of neural networks, neural architecture search problems and solution methods can be formulated under a common framework. Both practical and theoretical questions arise from closing the gap between applied neural architecture search and learning theory. Does structure make a difference or can it be chosen arbitrarily? This work is concerned with deep structures of artificial neural networks and examines automatic construction methods under empirical principles to shed light on to the so called ``black-box models''. Our contributions include a formulation of graph-induced neural networks that is used to pose optimisation problems for neural architecture. We analyse structural properties for different neural network objectives such as correctness, robustness or energy consumption and discuss how structure affects them. Selected automation methods for neural architecture optimisation problems are discussed and empirically analysed. With the insights gained from formalising graph-induced neural networks, analysing structural properties and comparing the applicability of neural architecture search methods qualitatively and quantitatively we advance these methods in two ways. First, new predictive models are presented for replacing computationally expensive evaluation schemes, and second, new generative models for informed sampling during neural architecture search are analysed and discussed.

AI Safety is an emerging area of critical importance to the safe adoption and deployment of AI systems. With the rapid proliferation of AI and especially with the recent advancement of Generative AI (or GAI), the technology ecosystem behind the design, development, adoption, and deployment of AI systems has drastically changed, broadening the scope of AI Safety to address impacts on public safety and national security. In this paper, we propose a novel architectural framework for understanding and analyzing AI Safety; defining its characteristics from three perspectives: Trustworthy AI, Responsible AI, and Safe AI. We provide an extensive review of current research and advancements in AI safety from these perspectives, highlighting their key challenges and mitigation approaches. Through examples from state-of-the-art technologies, particularly Large Language Models (LLMs), we present innovative mechanism, methodologies, and techniques for designing and testing AI safety. Our goal is to promote advancement in AI safety research, and ultimately enhance people's trust in digital transformation.