Active Measurement of Two-Point Correlations

Two-point correlation functions (2PCF) are often used to characterize how points cluster together. In this work, we are interested in measuring the 2PCF among a large number of points, but restricted to a subset that satisfies some 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 labeling. 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.