# Test Distribution-Aware Active Learning: A Principled Approach Against Distribution Shift and Outliers

arXiv: https://arxiv.org/abs/2106.11719 · HTML: https://mlsanity.com/paper/2106.11719/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 43 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [Be Your Own Teacher: Improve the Performance of Convolutional Neural Networks via Self Distillation](https://mlsanity.com/paper/1905.08094/) (2019)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Gone Fishing: Neural Active Learning with Fisher Embeddings](https://mlsanity.com/paper/2106.09675/) (2021)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [On Statistical Bias In Active Learning: How and When To Fix It](https://mlsanity.com/paper/2101.11665/) (2021)
- [Predictive Information Accelerates Learning in RL](https://mlsanity.com/paper/2007.12401/) (2020)
- [Beyond Marginal Uncertainty: How Accurately can Bayesian Regression Models Estimate Posterior Predictive Correlations?](https://mlsanity.com/paper/2011.03178/) (2020)

## Built on by (most cited first, 22 of 22)

- [Anchor Points: Benchmarking Models with Much Fewer Examples](https://mlsanity.com/paper/2309.08638/) (2023)
- [Active Learning Principles for In-Context Learning with Large Language Models](https://mlsanity.com/paper/2305.14264/) (2023)
- [Unifying Approaches in Active Learning and Active Sampling via Fisher Information and Information-Theoretic Quantities](https://mlsanity.com/paper/2208.00549/) (2022)
- [DiscoBAX: Discovery of Optimal Intervention Sets in Genomic Experiment Design](https://mlsanity.com/paper/2312.04064/) (2023)
- [Making Better Use of Unlabelled Data in Bayesian Active Learning](https://mlsanity.com/paper/2404.17249/) (2024)
- [Active Learning with Expected Error Reduction](https://mlsanity.com/paper/2211.09283/) (2022)
- [On the Limitations of Simulating Active Learning](https://mlsanity.com/paper/2305.13342/) (2023)
- [Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions](https://mlsanity.com/paper/2401.04305/) (2024)
- [Investigating Multi-source Active Learning for Natural Language Inference](https://mlsanity.com/paper/2302.06976/) (2023)
- [Training-Free Neural Active Learning with Initialization-Robustness Guarantees](https://mlsanity.com/paper/2306.04454/) (2023)
- [Marginal and Joint Cross-Entropies & Predictives for Online Bayesian Inference, Active Learning, and Active Sampling](https://mlsanity.com/paper/2205.08766/) (2022)
- [MoBYv2AL: Self-supervised Active Learning for Image Classification](https://mlsanity.com/paper/2301.01531/) (2023)
- [ASPEST: Bridging the Gap Between Active Learning and Selective Prediction](https://mlsanity.com/paper/2304.03870/) (2023)
- [Distributionally Robust Active Learning for Gaussian Process Regression](https://mlsanity.com/paper/2502.16870/) (2025)
- [Scalable Batch-Mode Deep Bayesian Active Learning via Equivalence Class Annealing](https://mlsanity.com/paper/2112.13737/) (2021)
- [Informed Initialization for Bayesian Optimization and Active Learning](https://mlsanity.com/paper/2510.23681/) (2025)
- [Learning Objective-Specific Active Learning Strategies with Attentive Neural Processes](https://mlsanity.com/paper/2309.05477/) (2023)
- [Batch Bayesian Active Learning with Partial Batch Label Sampling](https://mlsanity.com/paper/2510.09877/) (2025)
- [Beyond Binary Out-of-Distribution Detection: Characterizing Distributional Shifts with Multi-Statistic Diffusion Trajectories](https://mlsanity.com/paper/2510.17381/) (2025)
- [CAAL: Confidence-Aware Active Learning for Heteroscedastic Atmospheric Regression](https://mlsanity.com/paper/2602.11825/) (2026)
- [Active Learning for Gaussian Process Regression Under Self-Induced Boltzmann Weights](https://mlsanity.com/paper/2605.10654/) (2026)
- [NodeImport: Imbalanced Node Classification with Node Importance Assessment](https://mlsanity.com/paper/2607.13837/) (2026)

## Abstract (arXiv)

Expanding on MacKay (1992), we argue that conventional model-based methods for active learning - like BALD - have a fundamental shortfall: they fail to directly account for the test-time distribution of the input variables. This can lead to pathologies in the acquisition strategy, as what is maximally informative for model parameters may not be maximally informative for prediction: for example, when the data in the pool set is more dispersed than that of the final prediction task, or when the distribution of pool and test samples differs. To correct this, we revisit an acquisition strategy that is based on maximizing the expected information gained about possible future predictions, referring to this as the Expected Predictive Information Gain (EPIG). As EPIG does not scale well for batch acquisition, we further examine an alternative strategy, a hybrid between BALD and EPIG, which we call the Joint Expected Predictive Information Gain (JEPIG). We consider using both for active learning with Bayesian neural networks on a variety of datasets, examining the behavior under distribution shift in the pool set.