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Semi-Supervised Regression with Heteroscedastic Pseudo-Labels
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Proposes an uncertainty-aware pseudo-labeling framework for semi-supervised regression that learns per-sample pseudo-label log-variances via a bi-level optimization, with an efficient regression-head-only approximation.
Problem
Pseudo-labeling for semi-supervised regression is hard because continuous pseudo-labels carry heteroscedastic noise that is difficult to assess, so naive pseudo-labels cause error accumulation and overfitting to incorrect labels.
Approach
An uncertainty-learner network outputs per-pseudo-label log-variance and is optimized in an outer loop to minimize labeled-data loss of the regression model updated by an inner heteroscedastic weighted loss over labeled and pseudo-labeled data, with gradient unrolling restricted to the regression head.
Key results
- On UTKFace with 5% labels, MAE 5.639 vs. 5.719 for second-best RankUp (about 1.4% relative improvement).
- On IMDB-WIKI with 5% labels, MAE 9.177 and R^2 0.664, versus 9.730 MAE for UCVME (best of prior baselines near that setting).
- On STS-B with 5% labels, MSE 1.540 vs. 1.606 for SSDKL, with R^2 0.270 vs. 0.239; method adds about 9 ms per iteration and about 17 MB GPU memory over baseline on UTKFace.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use uncertainty-aware pseudo-labeling with bi-level optimization | Semi-supervised regression · UTKFace 5% labeled | MAE: 5.639 ± 0.035 vs 5.719 ± 0.112 | Helped |
| use uncertainty-aware pseudo-labeling with bi-level optimization | Semi-supervised regression · IMDB-WIKI 5% labeled | MAE: 9.177 ± 0.061 vs 9.492 ± 0.051 | Helped |
| use uncertainty-aware pseudo-labeling with bi-level optimization | Semi-supervised regression · STS-B 5% labeled | MSE: 1.540 ± 0.006 vs 1.606 ± 0.057 | Helped |
| add an uncertainty-learner without bi-level optimization (ablation) | Baseline SSR on IMDB-WIKI · 5% labeled | MAE: 9.512 -> 9.914 | Hurt |
| add bi-level optimization to the baseline plus uncertainty-learner (ablation) | Baseline + uncertainty-learner on IMDB-WIKI · 5% labeled | MAE: 9.914 -> 9.177 | Helped |
| add an uncertainty-learner without bi-level optimization (ablation) | Baseline SSR on IMDB-WIKI · 10% labeled | MAE: 8.864 -> 9.562 | Hurt |
| add bi-level optimization to the baseline plus uncertainty-learner (ablation) | Baseline + uncertainty-learner on IMDB-WIKI · 10% labeled | MAE: 9.562 -> 8.539 | Helped |
| add bi-level optimization to the baseline plus uncertainty-learner (ablation) | Baseline + uncertainty-learner on IMDB-WIKI · 5% labeled | R²: 0.630 -> 0.664 | Helped |
| add bi-level optimization to the baseline plus uncertainty-learner (ablation) | Baseline + uncertainty-learner on IMDB-WIKI · 10% labeled | R²: 0.651 -> 0.695 | Helped |
Surprising findings
- The uncertainty-learner used jointly (without bi-level optimization) performs worse than the baseline with fixed uncertainty on IMDB-WIKI.
- On UTKFace at 20% labels, UCVME outperforms the proposed method, which the authors attribute to stronger supervision improving pseudo-label quality.
Limitations
- Does not explicitly address systematic biases such as demographic imbalance in labeled or unlabeled data.
- Assumes labeled and unlabeled data are accessible simultaneously during training, raising privacy concerns.
- Gains diminish as the labeled fraction grows; UCVME and RankUp are better on UTKFace at 20% labels.
Experimental setup
Datasets: UTKFace IMDB-WIKI STS-B
Benchmarks: UTKFace IMDB-WIKI STS-B
Metrics: MAE R^2 MSE
Baselines: Supervised Mean Teacher Temporal Ensembling SSDKL TNNR SimRegMatch UCVME CLSS RankUp PIM UPS_Reg CADR
Builds on: FixMatch UCVME Mean Teacher Temporal Ensembling
Closest papers by meaning
- Keep It on a Leash: Controllable Pseudo-label Generation Towards Realistic Long-Tailed Semi-Supervised Learning (NeurIPS 2025 · similarity 0.91)
- Bi-Level Optimization for Semi-Supervised Learning with Pseudo-Labeling (AAAI 2025 · similarity 0.90)
- Rethinking Confidence Scores and Thresholds in Pseudolabeling-based SSL (ICML 2025 · similarity 0.88)
- Prediction-Powered Semi-Supervised Learning with Online Power Tuning (NeurIPS 2025 · similarity 0.88)
- Learning from Noisy Labels via Conditional Distributionally Robust Optimization (NeurIPS 2024 · similarity 0.87)
- Non-Stationary Predictions May Be More Informative: Exploring Pseudo-Labels with a Two-Phase Pattern of Training Dynamics (ICML 2025 · similarity 0.87)
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