# Active Cost-aware Labeling of Streaming Data

arXiv: https://arxiv.org/abs/2304.06808 · HTML: https://mlsanity.com/paper/2304.06808/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 13 Apr 2023.

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

- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Exploring Connections Between Active Learning and Model Extraction](https://mlsanity.com/paper/1811.02054/) (2018)
- [Minimax Analysis of Active Learning](https://mlsanity.com/paper/1410.0996/) (2014)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Active Learning of Linear Embeddings for Gaussian Processes](https://mlsanity.com/paper/1310.6740/) (2013)
- [Pool-Based Sequential Active Learning for Regression](https://mlsanity.com/paper/1805.04735/) (2018)
- [Multi-fidelity Gaussian Process Bandit Optimisation](https://mlsanity.com/paper/1603.06288/) (2016)
- [Convergence Rates of Active Learning for Maximum Likelihood Estimation](https://mlsanity.com/paper/1506.02348/) (2015)
- [Active Learning from Weak and Strong Labelers](https://mlsanity.com/paper/1510.02847/) (2015)
- [Neural Active Learning with Performance Guarantees](https://mlsanity.com/paper/2106.03243/) (2021)
- [Improved Algorithms for Neural Active Learning](https://mlsanity.com/paper/2210.00423/) (2022)
- [Near Optimal Bayesian Active Learning for Decision Making](https://mlsanity.com/paper/1402.5886/) (2014)
- [Near-optimal Bayesian Active Learning with Correlated and Noisy Tests](https://mlsanity.com/paper/1605.07334/) (2016)
- [Statistical Active Learning Algorithms for Noise Tolerance and Differential Privacy](https://mlsanity.com/paper/1307.3102/) (2013)
- [Query Efficient Posterior Estimation in Scientific Experiments via Bayesian Active Learning](https://mlsanity.com/paper/1702.01145/) (2017)
- [Splitting Gaussian Process Regression for Streaming Data](https://mlsanity.com/paper/2010.02424/) (2020)

## Built on by (most cited first, 3 of 3)

- [Sparse Semi-DETR: Sparse Learnable Queries for Semi-Supervised Object Detection](https://mlsanity.com/paper/2404.01819/) (2024)
- [Neural Active Learning Meets the Partial Monitoring Framework](https://mlsanity.com/paper/2405.08921/) (2024)
- [Gaussian Process Bandits for AI System Optimization with Selectively Verified Feedback](https://mlsanity.com/paper/2610.17760/) (2026)

## Abstract (arXiv)

We study actively labeling streaming data, where an active learner is faced with a stream of data points and must carefully choose which of these points to label via an expensive experiment. Such problems frequently arise in applications such as healthcare and astronomy. We first study a setting when the data's inputs belong to one of K discrete distributions and formalize this problem via a loss that captures the labeling cost and the prediction error. When the labeling cost is B, our algorithm, which chooses to label a point if the uncertainty is larger than a time and cost dependent threshold, achieves a worst-case upper bound of widetildeO(B^frac13 K^frac13 T^frac23) on the loss after T rounds. We also provide a more nuanced upper bound which demonstrates that the algorithm can adapt to the arrival pattern, and achieves better performance when the arrival pattern is more favorable. We complement both upper bounds with matching lower bounds. We next study this problem when the inputs belong to a continuous domain and the output of the experiment is a smooth function with bounded RKHS norm. After T rounds in d dimensions, we show that the loss is bounded by widetildeO(B^frac1d+3 T^fracd+2d+3) in an RKHS with a squared exponential kernel and by widetildeO(B^frac12d+3 T^frac2d+22d+3) in an RKHS with a Mat'ern kernel. Our empirical evaluation demonstrates that our method outperforms other baselines in several synthetic experiments and two real experiments in medicine and astronomy.