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In conventional statistical and machine learning methods, it is typically assumed that the test data are identically distributed with the training data. However, this assumption does not always hold, especially in applications where the target population are not well-represented in the training data. This is a notable issue in health-related studies, where specific ethnic populations may be underrepresented, posing a significant challenge for researchers aiming to make statistical inferences about these minority groups. In this work, we present a novel approach to addressing this challenge in linear regression models. We organize the model parameters for all the sub-populations into a tensor. By studying a structured tensor completion problem, we can achieve robust domain generalization, that is, learning about sub-populations with limited or no available data. Our method novelly leverages the structure of group labels and it can produce more reliable and interpretable generalization results. We establish rigorous theoretical guarantees for the proposed method and demonstrate its minimax optimality. To validate the effectiveness of our approach, we conduct extensive numerical experiments and a real data study focused on diabetes prediction for multiple subgroups, comparing our results with those obtained using other existing methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. 

Abstract SN 2023ehl, a normal Type Ia supernova with a typical decline rate, was discovered in the galaxy UGC 11555 and offers valuable insights into the explosion mechanisms of white dwarfs. We present a detailed analysis of SN 2023ehl, including spectroscopic and photometric observations. The supernova exhibits high-velocity features in its ejecta, which are crucial for understanding the physical processes during the explosion. We compared the light curves of SN 2023ehl with other well-observed Type Ia supernovae, finding similarities in their evolution. The line strength ratioR(Siii) was calculated to be 0.17 ± 0.04, indicating a higher photospheric temperature compared to other supernovae. The maximum quasi-bolometric luminosity was determined to be 1.52 × 10⁴³erg s⁻¹, and the synthesized⁵⁶Ni mass was estimated at 0.77 ± 0.05M_⊙. The photospheric velocity atB-band maximum light was measured as 10,150 ± 240 km s⁻¹, classifying SN 2023ehl as a normal velocity Type Ia supernova. Our analysis suggests that SN 2023ehl aligns more with both the gravitationally confined detonation, providing a comprehensive view of the diversity and complexity of Type Ia supernovae.