Machine learning models often underperform when the test data characteristics differ from the training data, a phenomenon known as domain shift. Improving robustness to domain shift has been a longstanding goal in machine learning, and is crucial to the widespread deployment of AI. This thesis addresses four underexplored but important aspects of this field: imbalanced domain adaptation, dataset filtering, model selection, and variance reduction of domain alignment losses. To this end, novel algorithms, perspectives, methodologies, and theoretical results are introduced, resulting in improved out-of-domain performance on these tasks. Particular emphasis is placed on developing methods that are both theoretically grounded and practically useful, and understanding their assumptions and limitations.A central motivating application for this work is the automated detection and classification of marine mammal vocalisations, where domain shift is especially prevalent. This thesis serves to underscore the importance of adopting robust training and evaluation practices in this context. To support progress in this area, a novel domain shift benchmark based on humpback whale detection is also introduced.Overall, this thesis contributes to advancing the reliability and trustworthiness of machine learning models, at a time when AI systems are increasingly being deployed to dynamic, uncertain, and open-ended settings
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