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Source-free unsupervised domain adaptation (SFUDA) aims to enable the utilization of a pre-trained source model in an unlabeled target domain without access to source data. Self-training is a way to solve SFUDA, where confident target samples are iteratively selected as pseudo-labeled samples to guide target model learning. However, prior heuristic noisy pseudo-label filtering methods all involve introducing extra models, which are sensitive to model assumptions and may introduce additional errors or mislabeling. In this work, we propose a method called Uncertainty-aware Pseudo-label-filtering Adaptation (UPA) to efficiently address this issue in a coarse-to-fine manner. Specially, we first introduce a sample selection module named Adaptive Pseudo-label Selection (APS), which is responsible for filtering noisy pseudo labels. The APS utilizes a simple sample uncertainty estimation method by aggregating knowledge from neighboring samples and confident samples are selected as clean pseudo-labeled. Additionally, we incorporate Class-Aware Contrastive Learning (CACL) to mitigate the memorization of pseudo-label noise by learning robust pair-wise representation supervised by pseudo labels. Through extensive experiments conducted on three widely used benchmarks, we demonstrate that our proposed method achieves competitive performance on par with state-of-the-art SFUDA methods. [ABSTRACT FROM AUTHOR]