Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Transductive Active Learning: Theory and Applications
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Generalizes active learning to transductive settings where prediction targets lie partly outside the sampleable region, proves uniform convergence rates for uncertainty-minimizing decision rules (VTL, ITL) under GP assumptions, and applies them to active fine-tuning and safe Bayesian optimization.
Problem
Active learning when the prediction targets are a specific set that may lie outside the accessible sample space, e.g. active fine-tuning toward a test set and safe Bayesian optimization where unsafe parameters must be inferred without being sampled.
Approach
Select samples within the sample space to minimize posterior uncertainty (variance or entropy) about prediction targets in a target space, yielding closed-form GP decision rules (VTL and ITL) whose uncertainty provably converges to the irreducible uncertainty, with rates governed by a target-dependent information capacity gamma_{A,S}(n).
Key results
- On active fine-tuning, ITL and VTL significantly outperform random selection and baselines on MNIST and CIFAR-100, retrieving more than twice the target-distribution samples as CosineSimilarity.
- In safe Bayesian optimization, ITL and VTL perform better than or on par with SafeOpt across synthetic 1d/2d tasks and a quadcopter controller tuning task, without violating safety constraints.
- Theory gives sigma_n^2(x) <= eta_S^2(x) + C gamma_{A,S}(n)/sqrt(n) uniformly over targets, and C' gamma_{A,S}(n)/n for targets inside the sample space.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TAL with ITL or VTL instead of uncertainty sampling | Gaussian process active learning · Synthetic GP experiments | target-space uncertainty | Helped |
| Use ITL or VTL instead of random sampling or the listed baselines | Active fine-tuning · MNIST | classification accuracy | Helped |
| Use ITL or VTL instead of random sampling or the listed baselines | Active fine-tuning · CIFAR-100 | classification accuracy | Helped |
| Use ITL or VTL instead of SafeOpt and ISE | Safe Bayesian optimization · Synthetic 1D and 2D tasks; quadcopter controller tuning | regret | Helped |
| Use VTL instead of ITL | Safe Bayesian optimization · Safe BO experiments | regret | Helped |
| Use ITL or VTL instead of CosineSimilarity | Active fine-tuning · MNIST and CIFAR-100 | rate of selecting samples from the target distribution | Helped |
| Use ITL rather than CosineSimilarity for batch selection | Active fine-tuning · MNIST and CIFAR-100 | classification accuracy | Helped |
| Use uncertainty-based TAL instead of EIC, which does not explicitly enforce safety | Safe Bayesian optimization · Safe BO experiments | constraint violations | Helped |
| Use the Gaussian kernel rather than the Laplace kernel (ablation) | ITL · Targeted GP sampling | information from points outside the target space | Mixed |
| Shrink the target-space volume relative to the domain (ablation) | ITL and VTL · Synthetic GP experiments | advantage over uncertainty sampling | Helped |
Surprising findings
- Transductive active learning outperforms random selection on MNIST even when the network is randomly initialized, suggesting embeddings are informative early in training.
- Output-space decision rules can exhibit strong synergies, so the submodularity assumption can fail; the Gaussian example shows information can be arbitrarily synergistic even when observations are uncorrelated.
Limitations
- Main convergence theory assumes submodularity of the uncertainty reduction, which is violated by some instances and holds only approximately in experiments.
- Analysis relies on known GP prior and noise variance (well-specified setting), with agnostic results using RKHS assumptions.
- Experiments are limited to MNIST, CIFAR-100 with a linear last-layer-style approximation and small synthetic and quadcopter safe BO tasks.
Experimental setup
Datasets: MNIST CIFAR-100 ImageNet
Benchmarks: MNIST CIFAR-100
Metrics: test accuracy regret constraint violation fraction of samples from target distribution
Baselines: Uncertainty sampling CosineSimilarity BADGE InformationDensity SafeOpt ISE EIC Random
Builds on: SafeOpt uncertainty sampling BALD mean-marginal information gain
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