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Although recent advances in machine learning have shown its success to learn from independent and identically distributed (IID) data, it is vulnerable to out-of-distribution (OOD) data in an open world. Domain generalization (DG) deals with such an issue and it aims to learn a model from multiple source domains that can be generalized to unseen target domains. Existing studies on DG have largely focused on stationary settings with homogeneous source domains. However, in many applications, domains may evolve along a specific direction (e.g., time, space). Without accounting for such non-stationary patterns, models trained with existing methods may fail to generalize on OOD data. In this paper, we study domain generalization in non-stationary environment. We first examine the impact of environmental non-stationarity on model performance and establish the theoretical upper bounds for the model error at target domains. Then, we propose a novel algorithm based on adaptive invariant representation learning, which leverages the non-stationary pattern to train a model that attains good performance on target domains. Experiments on both synthetic and real data validate the proposed algorithm. 

Abstract—Sleep staging is a key challenge in diagnosing and treating sleep-related diseases due to its labor-intensive, time- consuming, costly, and error-prone. With the availability of large- scale sleep signal data, many deep learning methods are proposed for automatic sleep staging. However, these existing methods face several challenges including the heterogeneity of patients’ underlying health conditions and the difficulty modeling complex interactions between sleep stages. In this paper, we propose a neural network architecture named DREAM to tackle these is- sues for automatic sleep staging. DREAM consists of (i) a feature representation network that generates robust representations for sleep signals via the variational auto-encoder framework and contrastive learning and (ii) a sleep stage classification network that explicitly models the interactions between sleep stages in the sequential context at both feature representation and label classification levels via Transformer and conditional random field architectures. Our experimental results indicate that DREAM significantly outperforms existing methods for automatic sleep staging on three sleep signal datasets.