Uncertainty-Calibrated Label Density Regularization for Few-Labeled Source-Free Regression Domain Adaptation

Few-labeled source-free regression adapts a pretrained regressor using scarce labeled target data and abundant unlabeled target inputs, without accessing source samples. Observed responses provide verified but sparse supervision, whereas predictions offer broader coverage but may be biased under domain shift. We propose Uncertainty-Calibrated Label Density Regularization (UCLDR), which uses predictions as uncertainty-regulated response evidence rather than directly fitting them as hard point-wise pseudo-labels. Uncertainty controls the admission, probability mass, and spread of predicted responses. The mixture supplies global mean–variance constraints, while its constituent assignments connect unlabeled features to labeled prototypes in overlapping response regions. This shared representation supports both forms of supervision without a separate trainable density model. At ten target labels, UCLDR achieves the lowest mean MSE on three of four benchmarks and the best average rank of 1.25 among the evaluated adaptation methods. On Cycle, it reduces mean MSE relative to CRAFT by 3.45–10.36% across five label budgets, with lower error on 7 to 11 of 12 transfers at each budget.