RELY: Beyond Deterministic Graphs for Uncertainty-Aware Crime Forecasting

Crime forecasting relies on dependencies among urban regions, but sparse event histories provide ambiguous evidence about which dependencies are reliable. A single deterministic graph commits to one structural estimate without explicitly representing this ambiguity, potentially allowing unreliable relations to influence predictions. We introduce RELY, a probabilistic structure learning framework that uses uncertainty in urban relations to guide spatiotemporal crime forecasting. RELY encodes geographic, functional, and historical information as probabilistic priors over pairwise links and regional group memberships. It refines these probabilities using each observation window and learns the resulting structures jointly with the forecasting model through differentiable sampling. To connect structural uncertainty with prediction, RELY derives reliability estimates for different relation channels and uses them to guide separate routing mechanisms for count intensity and excess-zero probability in a zero-inflated negative binomial decoder. This enables the two distributional components to draw on different combinations of relational evidence according to its estimated reliability. Experiments on Chicago and New York datasets show MAE reductions of 6.9% and 4.5%, respectively, over the strongest evaluated baselines, alongside improvements in RMSE and MAPE.