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  1. Hybrid modelling reduces the misspecification of expert models by combining them with machine learning (ML) components learned from data. Similarly to many ML algorithms, hybrid model performance guarantees are limited to the training distribution. Leveraging the insight that the expert model is usually valid even outside the training domain, we overcome this limitation by introducing a hybrid data augmentation strategy termed expert augmentation. Based on a probabilistic formalization of hybrid modelling, we demonstrate that expert augmentation, which can be incorporated into existing hybrid systems, improves generalization. We empirically validate the expert augmentation on three controlled experiments modelling dynamical systems with ordinary and partial differential equations. Finally, we assess the potential real-world applicability of expert augmentation on a dataset of a real double pendulum. 
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  2. Machine learning models are updated as new data is acquired or new architectures are developed. These updates usually increase model performance, but may introduce backward compatibility errors, where individual users or groups of users see their performance on the updated model adversely affected. This problem can also be present when training datasets do not accurately reflect overall population demographics, with some groups having overall lower participation in the data collection process, posing a significant fairness concern. We analyze how ideas from distributional robustness and minimax fairness can aid backward compatibility in this scenario, and propose two methods to directly address this issue. Our theoretical analysis is backed by experimental results on CIFAR-10, CelebA, and Waterbirds, three standard image classification datasets. 
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