Positive-unlabelled learning for recorded damp and mould risk in UK housing

Operational housing records identify damp-and-mould complaints and repairs, while dwellings without recorded events remain unlabelled rather than verified negatives. We formulate recorded damp-and-mould risk prioritisation as a Positive-Unlabelled (PU) learning problem using anonymised UK housing administrative data. The dataset contains 65,214 dwellings described by 291 property-level and household-level snapshot features, with 8,580 recorded positives and 56,634 unlabelled cases. We develop and evaluate a two-stage sample-selection PU framework: an out-of-fold XGBoost scorer first identifies conservative reliable negatives, and weighted Stage-2 classifiers then combine positives, reliable negatives, and weakly weighted residual unlabelled cases. The Stage-1 scorer achieved an out-of-fold development-set PU-AUC of 0.7547. The selected Stage-2 XGBoost model achieved a held-out PU-AUC of 0.7760 and average precision of 0.2981, and increased Recall@20% from 44.0% to 47.0%, retrieving 51 additional recorded positives compared with the Stage-1-only scorer. Supervised XGBoost baselines achieved similar recorded-label performance, while Stage-1 learner ablation showed that the framework supported alternative reliable-negative selectors. Grouped SHAP analysis connected the fitted scores to heating and fuel systems, household and occupancy context, assessment status, dwelling characteristics and energy performance. Targeted predictor exclusion reduced PU-AUC to 0.7648 and Recall@20% to 43.6%, quantifying dependence on selected inputs without resolving their temporal availability. These findings provide an empirical basis for PU-based recorded-risk prioritisation in housing, combining improved ranking over the initial scorer, explicit control over unlabelled training data and interpretation through housing-domain feature groups.