Unsupervised domain adaptation is a widespread set of methods that leverages the knowledge of a labeled source domain to train a model to perform well on a related unlabeled target domain. They generally introduce an auxiliary adaptation-related task that can be integrated into the multitask paradigm, which aims to merge multiple single-task models into a unified architecture. In this paper, we propose to associate domain adaptation and multitask balancing in the realistic context of an extreme class imbalance. Therefore, we propose a combined framework to cover and validate these approaches, and evaluate its performance in the physics-based context of the Cherenkov Telescope Array Observatory (CTAO). Along with a comparative study of some relevant adaptation techniques, we highlight the impact of extreme label shift and extend the investigations on importance weighting to rectify it. The complete code and results are published and available as open-source resources on Zenodo.

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