# Online Active Linear Regression via Thresholding

arXiv: https://arxiv.org/abs/1602.02845 · HTML: https://mlsanity.com/paper/1602.02845/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2016.

## Built on by (most cited first, 5 of 5)

- [Active learning for data streams: a survey](https://mlsanity.com/paper/2302.08893/) (2023)
- [Stream-based active learning with linear models](https://mlsanity.com/paper/2207.09874/) (2022)
- [Online Active Regression](https://mlsanity.com/paper/2207.05945/) (2022)
- [Robust online active learning](https://mlsanity.com/paper/2302.00422/) (2023)
- [QueryMarket: Cost-Aware Online Active Learning in Data Markets](https://mlsanity.com/paper/2606.17805/) (2026)

## Abstract (arXiv)

We consider the problem of online active learning to collect data for regression modeling. Specifically, we consider a decision maker with a limited experimentation budget who must efficiently learn an underlying linear population model. Our main contribution is a novel threshold-based algorithm for selection of most informative observations; we characterize its performance and fundamental lower bounds. We extend the algorithm and its guarantees to sparse linear regression in high-dimensional settings. Simulations suggest the algorithm is remarkably robust: it provides significant benefits over passive random sampling in real-world datasets that exhibit high nonlinearity and high dimensionality --- significantly reducing both the mean and variance of the squared error.