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Probability-Density-aware Semi-supervised Learning

AAAI 2025 · Label-efficient and robust learning › Semi-supervised learning · approach: Confidence-based pseudo-label selection · 3 citations (OpenAlex)

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Proposes a probability-density-aware similarity measure (PM) and a density-aware label propagation method (PMLP) that plugs into LASSL for semi-supervised image classification, with a theorem motivating the cluster assumption via KDE density along paths.

Problem

Existing semi-supervised learning methods rely on feature similarity for neighbor selection in label propagation and pseudo-labeling, and ignore the cluster assumption (points in different high-density regions belong to different classes), so unlabeled data is not fully exploited.

Approach

Reweight a traditional distance (first-order similarity, cosine, or Euclidean) by a KDE-based density measured along the straight line between two points, so that paths crossing low-density regions get lower affinity; prove that traditional label propagation is a special case (h to infinity) of this density-aware scheme.

Key results

• On CIFAR100 with 400 labels, PMLP+LASSL reaches 65.85% accuracy, +3.52% over LASSL and +1.21% over the second-best ShrinkMatch.
• On STL-10 with 40 labels, PMLP+LASSL reaches 85.53%, +3.96% over LASSL.
• On CIFAR10 with 40 labels, PMLP+LASSL gets 95.42% vs LASSL 95.07%; the SVHN 40-label gain is +0.94%.

Measured effects reported in the paper

Surprising findings

• Max and min density aggregation over path points are unstable across bandwidths, while average aggregation is stable.
• Several gains over LASSL are small (e.g., +0.05 on CIFAR10 with 250 labels), and PMLP underperforms some baselines on certain settings such as SVHN 40 labels.

Limitations

• Theorem 1 relies on sub-gaussian assumptions and asymptotic limits (large mean separation), which may not hold for real features.
• Performance is sensitive to the KDE bandwidth and the choice of density aggregation; the authors note an incorrect early density prior can mislead training.
• Density is estimated along straight lines with a small number of sampled points, and high-dimensional KDE remains costly.

Experimental setup

Datasets: SVHN CIFAR10 CIFAR100 STL-10

Benchmarks: SVHN CIFAR10 CIFAR100 STL-10

Metrics: accuracy standard deviation over 5 runs running time per epoch pseudo-label accuracy

Baselines: Pseudo-label Mean-Teacher MixMatch UDA ReMixMatch FixMatch ReFixMatch SoftMatch EPASS FreeMatch ShrinkMatch LASSL

Builds on: LASSL label propagation (Zhou et al. 2003) FixMatch class-aware contrastive learning

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• Density-Aware Graph for Deep Semi-Supervised Visual Recognition (CVPR 2020 · similarity 0.89)
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