Reducing bias in source-free unsupervised domain adaptation for regression.

Due to data privacy and storage concerns, Source-Free Unsupervised Domain Adaptation (SFUDA) focuses on improving an unlabelled target domain by leveraging a pre-trained source model without access to source data. While existing studies attempt to train target models by mitigating biases induced by noisy pseudo labels, they often lack theoretical guarantees for fully reducing biases and have predominantly addressed classification tasks rather than regression ones. To address these gaps, our analysis delves into the generalisation error bound of the target model, aiming to understand the intrinsic limitations of pseudo-label-based SFUDA methods. Theoretical results reveal that biases influencing generalisation error extend beyond the commonly highlighted label inconsistency bias, which denotes the mismatch between pseudo labels and ground truths, and the feature-label mapping bias, which represents the difference between the proxy target regressor and the real target regressor. Equally significant is the feature misalignment bias, indicating the misalignment between the estimated and real target feature distributions. This factor is frequently neglected or not explicitly addressed in current studies. Additionally, the label inconsistency bias can be unbounded in regression due to the continuous label space, further complicating SFUDA for regression tasks. Guided by these theoretical insights, we propose a Bias-Reduced Regression (BRR) method for SFUDA in regression. This method incorporates Feature Distribution Alignment (FDA) to reduce the feature misalignment bias, Hybrid Reliability Evaluation (HRE) to reduce the feature-label mapping bias and pseudo label updating to mitigate the label inconsistency bias. Experiments demonstrate the superior performance of the proposed BRR, and the effectiveness of FDA and HRE in reducing biases for regression tasks in SFUDA.