# Active Learning with Expected Error Reduction

arXiv: https://arxiv.org/abs/2211.09283 · HTML: https://mlsanity.com/paper/2211.09283/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [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)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Variational Adversarial Active Learning](https://mlsanity.com/paper/1904.00370/) (2019)
- [Accuracy on the Line: On the Strong Correlation Between Out-of-Distribution and In-Distribution Generalization](https://mlsanity.com/paper/2107.04649/) (2021)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [The iWildCam 2020 Competition Dataset](https://mlsanity.com/paper/2004.10340/) (2020)
- [Active Learning under Label Shift](https://mlsanity.com/paper/2007.08479/) (2020)
- [Test Distribution-Aware Active Learning: A Principled Approach Against Distribution Shift and Outliers](https://mlsanity.com/paper/2106.11719/) (2021)

## Built on by (most cited first, 9 of 9)

- [LabelBench: A Comprehensive Framework for Benchmarking Adaptive Label-Efficient Learning](https://mlsanity.com/paper/2306.09910/) (2023)
- [A Short Survey on Importance Weighting for Machine Learning](https://mlsanity.com/paper/2403.10175/) (2024)
- [When Self-Belief Misleads: Active Label Acquisition for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2605.25864/) (2026)
- [Learning to Rank for Active Learning via Multi-Task Bilevel Optimization](https://mlsanity.com/paper/2310.17044/) (2023)
- [Direct Acquisition Optimization for Low-Budget Active Learning](https://mlsanity.com/paper/2402.06045/) (2024)
- [Active Learning of Deep Neural Networks via Gradient-Free Cutting Planes](https://mlsanity.com/paper/2410.02145/) (2024)
- [Batch Bayesian Active Learning with Partial Batch Label Sampling](https://mlsanity.com/paper/2510.09877/) (2025)
- [The Approximation Ratio for the Risk of Myopic Bayesian Active Learning for Linear Regression](https://mlsanity.com/paper/2607.06642/) (2026)
- [Large Classification-Risk-Optional Label Acquisition](https://mlsanity.com/paper/2609.06873/) (2026)

## Abstract (arXiv)

Active learning has been studied extensively as a method for efficient data collection. Among the many approaches in literature, Expected Error Reduction (EER) (Roy and McCallum) has been shown to be an effective method for active learning: select the candidate sample that, in expectation, maximally decreases the error on an unlabeled set. However, EER requires the model to be retrained for every candidate sample and thus has not been widely used for modern deep neural networks due to this large computational cost. In this paper we reformulate EER under the lens of Bayesian active learning and derive a computationally efficient version that can use any Bayesian parameter sampling method (such as arXiv:1506.02142). We then compare the empirical performance of our method using Monte Carlo dropout for parameter sampling against state of the art methods in the deep active learning literature. Experiments are performed on four standard benchmark datasets and three WILDS datasets (arXiv:2012.07421). The results indicate that our method outperforms all other methods except one in the data shift scenario: a model dependent, non-information theoretic method that requires an order of magnitude higher computational cost (arXiv:1906.03671).