Positive-Unlabeled Learning for Control Group Construction in Observational Causal Inference

Abstract

In causal inference, whether through randomized controlled trials or observational studies, access to both treated and control units is essential for estimating the effect of a treatment on an outcome of interest. When treatment assignment is random, the average treatment effect (ATE) can be estimated directly by comparing outcomes between groups. In non-randomized settings, various techniques are employed to adjust for confounding and approximate the counterfactual scenario to recover an unbiased ATE. A common challenge, especially in observational studies, is the absence of units clearly labeled as controls-that is, units known not to have received the treatment. To address this, we propose positive-unlabeled (PU) learning as a framework for identifying, with high confidence, control units from a pool of unlabeled ones, using only the available treated (positive) units. We evaluate this approach using both simulated and real-world data. We construct a causal graph with diverse relationships and use it to generate synthetic data under various scenarios, assessing how reliably the method recovers control groups that allow estimates of true ATE. We also apply our approach to real-world data on optimal sowing and fertilizer treatments in sustainable agriculture. Our findings show that PU learning can successfully identify control (negative) units from unlabeled data based only on treated units and, through the resulting control group, estimate an ATE that closely approximates the true value. This work has important implications for observational causal inference, especially in fields where randomized experiments are difficult or costly. In domains such as earth, environmental, and agricultural sciences, it enables a plethora of quasi-experiments by leveraging available earth observation and climate data, particularly when treated units are available but control units are lacking.