Reasoning about a model's accuracy on a test sample from its confidence is a central problem in machine learning, being connected to important applications such as uncertainty representation, model selection, and exploration. While these connections have been well-studied in the i.i.d. settings, distribution shifts pose significant challenges to the traditional methods. Therefore, model calibration and model selection remain challenging in the unsupervised domain adaptation problem--a scenario where the goal is to perform well in a distribution shifted domain without labels. In this work, we tackle difficulties coming from distribution shifts by developing a novel importance weighted group accuracy estimator. Specifically, we formulate an optimization problem for finding an importance weight that leads to an accurate group accuracy estimation in the distribution shifted domain with theoretical analyses. Extensive experiments show the effectiveness of group accuracy estimation on model calibration and model selection. Our results emphasize the significance of group accuracy estimation for addressing challenges in unsupervised domain adaptation, as an orthogonal improvement direction with improving transferability of accuracy.

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