# On Statistical Bias In Active Learning: How and When To Fix It

arXiv: https://arxiv.org/abs/2101.11665 · HTML: https://mlsanity.com/paper/2101.11665/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 55 references that are in the map.
- First posted on arXiv 27 Jan 2021.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [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)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [Selection via Proxy: Efficient Data Selection for Deep Learning](https://mlsanity.com/paper/1906.11829/) (2019)
- [Learning Loss for Active Learning](https://mlsanity.com/paper/1905.03677/) (2019)
- [Variational Adversarial Active Learning](https://mlsanity.com/paper/1904.00370/) (2019)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Cost-Effective Active Learning for Deep Image Classification](https://mlsanity.com/paper/1701.03551/) (2017)
- [Deep Active Learning for Named Entity Recognition](https://mlsanity.com/paper/1707.05928/) (2017)
- [Deep Bayesian Active Learning for Natural Language Processing: Results of a Large-Scale Empirical Study](https://mlsanity.com/paper/1808.05697/) (2018)
- [Practical Obstacles to Deploying Active Learning](https://mlsanity.com/paper/1807.04801/) (2018)
- [Active Learning for Cost-Sensitive Classification](https://mlsanity.com/paper/1703.01014/) (2017)
- [Active Learning with Partial Feedback](https://mlsanity.com/paper/1802.07427/) (2018)
- [Half a Percent of Labels is Enough: Efficient Animal Detection in UAV Imagery using Deep CNNs and Active Learning](https://mlsanity.com/paper/1907.07319/) (2019)
- [Bayesian semi-supervised learning for uncertainty-calibrated prediction of molecular properties and active learning](https://mlsanity.com/paper/1902.00925/) (2019)
- [Cost-Effective Training of Deep CNNs with Active Model Adaptation](https://mlsanity.com/paper/1802.05394/) (2018)
- [Active Learning for Decision-Making from Imbalanced Observational Data](https://mlsanity.com/paper/1904.05268/) (2019)
- [Active Testing: An Efficient and Robust Framework for Estimating Accuracy](https://mlsanity.com/paper/1807.00493/) (2018)
- [Leveraging Crowdsourcing Data For Deep Active Learning - An Application: Learning Intents in Alexa](https://mlsanity.com/paper/1803.04223/) (2018)
- [Active Learning with Logged Data](https://mlsanity.com/paper/1802.09069/) (2018)

## Built on by (most cited first, 30 of 75)

- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Anchor Points: Benchmarking Models with Much Fewer Examples](https://mlsanity.com/paper/2309.08638/) (2023)
- [Active Testing: Sample-Efficient Model Evaluation](https://mlsanity.com/paper/2103.05331/) (2021)
- [A Survey on Deep Active Learning: Recent Advances and New Frontiers](https://mlsanity.com/paper/2405.00334/) (2024)
- [A Framework and Benchmark for Deep Batch Active Learning for Regression](https://mlsanity.com/paper/2203.09410/) (2022)
- [Stochastic Batch Acquisition: A Simple Baseline for Deep Active Learning](https://mlsanity.com/paper/2106.12059/) (2021)
- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)
- [Active Surrogate Estimators: An Active Learning Approach to Label-Efficient Model Evaluation](https://mlsanity.com/paper/2202.06881/) (2022)
- [A Lagrangian Duality Approach to Active Learning](https://mlsanity.com/paper/2202.04108/) (2022)
- [Test Distribution-Aware Active Learning: A Principled Approach Against Distribution Shift and Outliers](https://mlsanity.com/paper/2106.11719/) (2021)
- [General Intelligence Requires Rethinking Exploration](https://mlsanity.com/paper/2211.07819/) (2022)
- [Class-Balanced Active Learning for Image Classification](https://mlsanity.com/paper/2110.04543/) (2021)
- [A Short Survey on Importance Weighting for Machine Learning](https://mlsanity.com/paper/2403.10175/) (2024)
- [Active Learning in Bayesian Neural Networks with Balanced Entropy Learning Principle](https://mlsanity.com/paper/2105.14559/) (2021)
- [Breaking Feedback Loops in Recommender Systems with Causal Inference](https://mlsanity.com/paper/2207.01616/) (2022)
- [Controllable Textual Inversion for Personalized Text-to-Image Generation](https://mlsanity.com/paper/2304.05265/) (2023)
- [A Framework for Efficient Model Evaluation through Stratification, Sampling, and Estimation](https://mlsanity.com/paper/2406.07320/) (2024)
- [Scaling Up Active Testing to Large Language Models](https://mlsanity.com/paper/2508.09093/) (2025)
- [D-CALM: A Dynamic Clustering-based Active Learning Approach for Mitigating Bias](https://mlsanity.com/paper/2305.17013/) (2023)
- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [Gaussian Switch Sampling: A Second Order Approach to Active Learning](https://mlsanity.com/paper/2302.12018/) (2023)
- [Characterizing the robustness of Bayesian adaptive experimental designs to active learning bias](https://mlsanity.com/paper/2205.13698/) (2022)
- [Consensus-Driven Active Model Selection](https://mlsanity.com/paper/2507.23771/) (2025)
- [MultiBreak: A Scalable and Diverse Multi-turn Jailbreak Benchmark for Evaluating LLM Safety](https://mlsanity.com/paper/2605.01687/) (2026)
- [Prioritized training on points that are learnable, worth learning, and not yet learned (workshop version)](https://mlsanity.com/paper/2107.02565/) (2021)
- [Metrics for Bayesian Optimal Experiment Design under Model Misspecification](https://mlsanity.com/paper/2304.07949/) (2023)
- [Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions](https://mlsanity.com/paper/2401.04305/) (2024)
- [Bayesian Active Learning in the Presence of Nuisance Parameters](https://mlsanity.com/paper/2310.14968/) (2023)

## Abstract (arXiv)

Active learning is a powerful tool when labelling data is expensive, but it introduces a bias because the training data no longer follows the population distribution. We formalize this bias and investigate the situations in which it can be harmful and sometimes even helpful. We further introduce novel corrective weights to remove bias when doing so is beneficial. Through this, our work not only provides a useful mechanism that can improve the active learning approach, but also an explanation of the empirical successes of various existing approaches which ignore this bias. In particular, we show that this bias can be actively helpful when training overparameterized models -- like neural networks -- with relatively little data.