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Positive and Unlabeled Learning with Controlled Probability Boundary Fence

ICML 2024 · Label-efficient and robust learning › Recognition and long-tail · approach: Learning from unlabeled and positive-unlabeled data

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Proposes PUL-CPBF, a two-stage PU learning method that uses a set of weak classifiers trained with asymmetric disambiguation-free risks as a probability boundary fence to assign stochastic labels to unlabeled data, then self-trains a strong classifier.

Problem

Positive and unlabeled (PU) learning: inducing a binary classifier from few labeled positives and many unlabeled instances, where naive disambiguation-free risk suffers boundary deviation toward the positive side.

Approach

A theorem shows the probability boundary alpha of the asymmetric disambiguation-free risk is controlled by its asymmetric penalty beta; multiple weak classifiers at different alpha values form a probability boundary fence that yields stochastic labels for unlabeled instances, which then train a strong classifier via self-training.

Key results

• PUL-CPBF achieves the highest accuracy among PU baselines on all six benchmark PU settings, e.g., 96.7 on F-MNIST-1 and 91.4 on CIFAR-10-1, improving on HolisticPU by about 0.9 and 1.3 on STL-10-1 and STL-10-2.
• On the Alzheimer dataset PUL-CPBF reports 73.4 accuracy and 81.1 AUC, comparable to SOTA baselines DistPU and HolisticPU.
• PUL-CPBF runs faster than HolisticPU (e.g., 421 s vs 761 s on STL-10-1) while being slower than Dist-PU, since only classification layers are optimized with a frozen pre-trained backbone.

Measured effects reported in the paper

Surprising findings

• The asymmetric risk with the theoretically optimal beta (alpha=0.5) did not perform best; alpha=0.3 outperformed it on FashionMNIST-1, which the authors attribute to surrogate loss and class-prior estimation errors.

Limitations

• Theorem relies on the disambiguation-free risk and logistic surrogate loss; the theoretical optimal beta is not always the best empirically.
• Class prior and bpi estimation (KM2 and labeled proportion) may be inaccurate, causing theory-practice gaps.
• Performance remains below the PN learning upper bound by about 0.5 to 2.6 points.

Experimental setup

Datasets: F-MNIST CIFAR-10 STL-10 Alzheimer

Benchmarks: F-MNIST-1 F-MNIST-2 CIFAR-10-1 CIFAR-10-2 STL-10-1 STL-10-2 Alzheimer

Metrics: classification accuracy F1 score recall precision AUC

Baselines: uPU nnPU Self-PU VPU PULNS PAN Dist-PU P3Mix Robust-PU HolisticPU PN learning

Builds on: uPU nnPU P3Mix FixMatch-style consistency regularization (Sohn et al., 2020) asymmetric risk (Scott, 2012)

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