Semi-Supervised Regression with Heteroscedastic Pseudo-Labels

Pseudo-labeling is a commonly used paradigm in semi-supervised learning, yet its application to semi-supervised regression (SSR) remains relatively under-explored. Unlike classification, where pseudo-labels are discrete and confidence-based filtering is effective, SSR involves continuous outputs with heteroscedastic noise, making it challenging to assess pseudo-label reliability. As a result, naive pseudo-labeling can lead to error accumulation and overfitting to incorrect labels. To address this, we propose an uncertainty-aware pseudo-labeling framework that dynamically adjusts pseudo-label influence from a bi-level optimization perspective. By jointly minimizing empirical risk over all data and optimizing uncertainty estimates to enhance generalization on labeled data, our method effectively mitigates the impact of unreliable pseudo-labels. We provide theoretical insights and extensive experiments to validate our approach across various benchmark SSR datasets, and the results demonstrate superior robustness and performance compared to existing methods. Our code is available at https://github.com/sxq/Heteroscedastic-Pseudo-Labels.