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Semi-Supervised Regression with Heteroscedastic Pseudo-Labels

NeurIPS 2025 · Label-efficient and robust learning › Semi-supervised learning · approach: Confidence-based pseudo-label selection · 1 citations (OpenAlex)

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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

Measured effects reported in the paper

What was changedWhereMeasuredEffect
use uncertainty-aware pseudo-labeling with bi-level optimizationSemi-supervised regression · UTKFace 5% labeledMAE: 5.639 ± 0.035 vs 5.719 ± 0.112Helped
use uncertainty-aware pseudo-labeling with bi-level optimizationSemi-supervised regression · IMDB-WIKI 5% labeledMAE: 9.177 ± 0.061 vs 9.492 ± 0.051Helped
use uncertainty-aware pseudo-labeling with bi-level optimizationSemi-supervised regression · STS-B 5% labeledMSE: 1.540 ± 0.006 vs 1.606 ± 0.057Helped
add an uncertainty-learner without bi-level optimization (ablation)Baseline SSR on IMDB-WIKI · 5% labeledMAE: 9.512 -> 9.914Hurt
add bi-level optimization to the baseline plus uncertainty-learner (ablation)Baseline + uncertainty-learner on IMDB-WIKI · 5% labeledMAE: 9.914 -> 9.177Helped
add an uncertainty-learner without bi-level optimization (ablation)Baseline SSR on IMDB-WIKI · 10% labeledMAE: 8.864 -> 9.562Hurt
add bi-level optimization to the baseline plus uncertainty-learner (ablation)Baseline + uncertainty-learner on IMDB-WIKI · 10% labeledMAE: 9.562 -> 8.539Helped
add bi-level optimization to the baseline plus uncertainty-learner (ablation)Baseline + uncertainty-learner on IMDB-WIKI · 5% labeledR²: 0.630 -> 0.664Helped
add bi-level optimization to the baseline plus uncertainty-learner (ablation)Baseline + uncertainty-learner on IMDB-WIKI · 10% labeledR²: 0.651 -> 0.695Helped

Surprising findings

Limitations

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

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