# Active Measurement of Two-Point Correlations

arXiv: https://arxiv.org/abs/2604.05227 · HTML: https://mlsanity.com/paper/2604.05227/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 6 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [IS-COUNT: Large-scale Object Counting from Satellite Images with Covariate-based Importance Sampling](https://mlsanity.com/paper/2112.09126/) (2021)
- [DISCount: Counting in Large Image Collections with Detector-Based Importance Sampling](https://mlsanity.com/paper/2306.03151/) (2023)
- [Human-in-the-Loop Visual Re-ID for Population Size Estimation](https://mlsanity.com/paper/2312.05287/) (2023)
- [Active Measurement: Efficient Estimation at Scale](https://mlsanity.com/paper/2507.01372/) (2025)
- [Leveraging Importance Weights in Subset Selection](https://mlsanity.com/paper/2301.12052/) (2023)
- [StarcNet: Machine Learning for Star Cluster Identification](https://mlsanity.com/paper/2012.09327/) (2020)

## Abstract (arXiv)

Two-point correlation functions (2PCF) are widely used to characterize how points cluster in space. In this work, we study the problem of measuring the 2PCF over a large set of points, restricted to a subset satisfying a property of interest. An example comes from astronomy, where scientists measure the 2PCF of star clusters, which make up only a tiny subset of possible sources within a galaxy. This task typically requires careful labeling of sources to construct catalogs, which is time-consuming. We present a human-in-the-loop framework for efficient estimation of 2PCF of target sources. By leveraging a pre-trained classifier to guide sampling, our approach adaptively selects the most informative points for human annotation. After each annotation, it produces unbiased estimates of pair counts across multiple distance bins simultaneously. Compared to simple Monte Carlo approaches, our method achieves substantially lower variance while significantly reducing annotation effort. We introduce a novel unbiased estimator, sampling strategy, and confidence interval construction that together enable scalable and statistically grounded measurement of two-point correlations in astronomy datasets.