# Active Regression by Stratification

arXiv: https://arxiv.org/abs/1410.5920 · HTML: https://mlsanity.com/paper/1410.5920/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2014.

## Built on by (most cited first, 8 of 8)

- [Differentiable Learning Under Triage](https://mlsanity.com/paper/2103.08902/) (2021)
- [Active Surrogate Estimators: An Active Learning Approach to Label-Efficient Model Evaluation](https://mlsanity.com/paper/2202.06881/) (2022)
- [Online Active Regression](https://mlsanity.com/paper/2207.05945/) (2022)
- [Query Complexity of Active Learning for Function Family With Nearly Orthogonal Basis](https://mlsanity.com/paper/2306.03356/) (2023)
- [Streaming Active Learning for Regression Problems Using Regression via Classification](https://mlsanity.com/paper/2309.01013/) (2023)
- [Targeted active learning for probabilistic models](https://mlsanity.com/paper/2210.12122/) (2022)
- [Near-Polynomially Competitive Active Logistic Regression](https://mlsanity.com/paper/2503.05981/) (2025)
- [QueryMarket: Cost-Aware Online Active Learning in Data Markets](https://mlsanity.com/paper/2606.17805/) (2026)

## Abstract (arXiv)

We propose a new active learning algorithm for parametric linear regression with random design. We provide finite sample convergence guarantees for general distributions in the misspecified model. This is the first active learner for this setting that provably can improve over passive learning. Unlike other learning settings (such as classification), in regression the passive learning rate of O(1/ε) cannot in general be improved upon. Nonetheless, the so-called `constant' in the rate of convergence, which is characterized by a distribution-dependent risk, can be improved in many cases. For a given distribution, achieving the optimal risk requires prior knowledge of the distribution. Following the stratification technique advocated in Monte-Carlo function integration, our active learner approaches the optimal risk using piecewise constant approximations.