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SEL-BALD: Deep Bayesian Active Learning with Selective Labels
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Studies active learning when humans can reject labeling requests (selective labels), and proposes SEL-BALD acquisition functions (e-BALD, Joint-BALD, Joint-BALD-UCB/TS) that jointly target model information gain and human discretion-model information gain.
Problem
Active learning in high-stakes settings where human experts may decline to label instances selected by the model, so labels are selectively observed and conventional acquisition wastes examination budget.
Approach
Weights the BALD mutual-information objective by the estimated probability that a human will label an instance, and adds an information-gain term about a Bayesian human-discretion model, with UCB or Thompson-sampling variants to balance exploration and exploitation of the discretion model.
Key results
- On the synthetic two-circle data, Joint-BALD-UCB and Joint-BALD-TS reach accuracy 0.99 and 0.98 versus 0.78 for RANDOM and 0.55 for Naive-BALD at budget 450.
- On GMC and MNIST, Joint-BALD-UCB and Joint-BALD-TS outperform Naive-BALD and RANDOM across budgets, which spend most of the budget on examinations that are rejected.
- Under homogeneous discretion (e(x)=0.8 on MNIST), all SEL-BALD variants perform similarly, consistent with the theory that ALIR reduces to standard active learning.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Joint-BALD-UCB instead of Naive-BALD | SEL-BALD active learning · Synthetic data | accuracy: 0.55 -> 0.99 | Helped |
| Use Joint-BALD-TS instead of Naive-BALD | SEL-BALD active learning · Synthetic data | accuracy: 0.55 -> 0.98 | Helped |
| Model human discretion and explore its uncertainty with Joint-BALD-UCB | SEL-BALD active learning · Give-Me-some-Credit (GMC) | accuracy | Helped |
| Model human discretion and explore its uncertainty with Joint-BALD-TS | SEL-BALD active learning · MNIST | accuracy | Helped |
| Use Naive-BALD rather than Joint-BALD-UCB | Active learning with instance rejection · Synthetic data | accuracy: 0.99 -> 0.55 | Hurt |
| Use RANDOM rather than Joint-BALD-UCB | Active learning with instance rejection · Synthetic data | accuracy: 0.99 -> 0.78 | Hurt |
| Use e-BALD rather than Joint-BALD-UCB | SEL-BALD active learning · Synthetic data | accuracy: 0.99 -> 0.76 | Hurt |
| Use e-BALD with a noisy human-discretion estimate instead of Joint-BALD-UCB | SEL-BALD active learning · Synthetic data | accuracy: 0.99 -> 0.76 | Hurt |
| Use Joint-BALD rather than Joint-BALD-UCB | SEL-BALD active learning · Synthetic data | accuracy: 0.99 -> 0.77 | Hurt |
| Use BALD rather than Joint-BALD-UCB under changing human behavior | Active learning with instance rejection · Synthetic two-moons data | accuracy | Hurt |
| Use Joint-BALD-UCB rather than Naive-BALD with a logistic-regression human behavior model | SEL-BALD active learning · Adult | accuracy | Helped |
| Replace information gain with entropy and use Joint-Entropy-UCB (ablation) | Entropy-based active learning · Synthetic data | accuracy | Helped |
Surprising findings
- e-BALD, which greedily targets likely-labeled instances, can underperform Naive-BALD-like baselines at larger budgets because of noisy discretion-model estimates.
- RANDOM is a strong baseline on the Mushroom dataset in the batch setting, per the ML-based human behavior appendix.
Limitations
- Assumes all humans share a single discretion model rather than heterogeneous decision makers.
- Performance depends on correct specification of the human discretion model class; misspecification can bias acquisition.
- Fairness implications of prioritizing labeled instances are not addressed and the method may not apply in some settings.
Experimental setup
Datasets: Give-Me-Some-Credit MNIST Fashion-MNIST CIFAR-10 Adult Mushroom synthetic two-circle synthetic two-moon
Benchmarks: Give-Me-Some-Credit MNIST Fashion-MNIST CIFAR-10 Adult Mushroom synthetic two-circle
Metrics: accuracy number of labeled samples examination and labeling budget fraction
Baselines: RANDOM Naive-BALD e-BALD Joint-BALD
Builds on: BALD MC dropout UCB Thompson sampling
Closest papers by meaning
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- Uncertainty Herding: One Active Learning Method for All Label Budgets (ICLR 2025 · similarity 0.84)
- Regretful Decisions under Label Noise (ICLR 2025 · similarity 0.84)
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- Adaptive Labeling for Efficient Out-of-distribution Model Evaluation (NeurIPS 2024 · similarity 0.83)
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