Abstract: Test-time adaptation (TTA) adapts a source model to the distribution shift in testing data without using any source data. There have been plenty of algorithms concentrated on covariate shift in the last decade, i.e., $\mathcal{D}_t(X)$, the distribution of the test data is different from the source data. Nonetheless, in real application scenarios, it is necessary to consider the influence of label distribution shift, i.e., both $\mathcal{D}_t(X)$ and $\mathcal{D}_t(Y)$ are shifted, which has not been sufficiently explored yet. To remedy this, we study a new problem setup, namely, TTA with Open-world Data Shift (AODS). The goal of AODS is simultaneously adapting a model to covariate and label distribution shifts in the test phase. In this paper, we first analyze the relationship between classification error and distribution shifts. Motivated by this, we hence propose a new framework, namely ODS, which decouples the mixed distribution shift and then addresses covariate and label distribution shifts accordingly. We conduct experiments on multiple benchmarks with different types of shifts, and the results demonstrate the superior performance of our method against the state of the arts. Moreover, ODS is suitable for many TTA algorithms.