Assessing Predictive Models for Fairness Based on Activity-Space Patterns

Predictive policing systems that allocate patrol resources based solely on predicted crime risk can unintentionally amplify racial disparities through feedback driven data bias. We present FASE, a Fairness Aware Spatiotemporal Event Graph framework, which integrates spatiotemporal crime prediction with fairness constrained patrol allocation and a closed loop deployment feedback simulator. We model Baltimore as a graph of 25 ZIP Code Tabulation Areas and use 139,982 Part 1 crime incidents from 2017 to 2019 at hourly resolution, producing a sparse feature tensor. The prediction module combines a spatiotemporal graph neural network with a multivariate Hawkes process to capture spatial dependencies and self exciting temporal dynamics. Outputs are modeled using a Zero Inflated Negative Binomial distribution, suitable for overdispersed and zero heavy crime counts. The model achieves a validation loss of 0.4800 and a test loss of 0.4857. Patrol allocation is formulated as a fairness constrained linear optimization problem that maximizes risk weighted coverage while enforcing a Demographic Impact Ratio constraint with deviation bounded by 0.05. Across six simulated deployment cycles, fairness remains within 0.9928 to 1.0262, and coverage ranges from 0.876 to 0.936. However, a persistent detection rate gap of approximately 3.5 percentage points remains between minority and non minority areas. This result shows that allocation level fairness constraints alone do not eliminate feedback induced bias in retraining data, highlighting the need for fairness interventions across the full pipeline.

Fairness-accuracy trade-offs are a central concern in the deployment of fairness-aware machine learning methods. When sensitive attributes are unavailable at inference time-the so called unawareness setting, principled methods for obtaining accurate predictions under relaxed fairness constraints are largely missing. In this work, we address this gap by formulating regression under a demographic parity penalty as an optimal transport problem. Our framework unifies both the \emph{aware} and \emph{unaware} settings and characterizes optimal prediction functions via optimal transport maps, under both squared Wasserstein-2 and Total Variation penalties. These results reveal that the choice of penalty reflects fundamentally different fairness philosophies: the Wasserstein penalty induces a smooth, population-wide compromise, while Total Variation enforces exact parity for a subset of individuals. Building on these theoretical characterizations, we propose an algorithm that is simple to implement, computationally efficient, and consistently matches or outperforms state-of-the-art baselines on real-world benchmarks.

Individual fairness, the notion that "similar individuals should be treated similarly," provides a strong and flexible fairness guarantee for algorithmic decision makers. However, a barrier to implementing individual fairness in practice is the difficulty of learning the similarity metric over individuals. In this work, we present an algorithm for learning a Mahalanobis similarity metric from triplet queries of the form "is individual $i$ more similar to individual $j$ or $k$?" We work in the standard Bradley-Terry model for pairwise comparisons. Our algorithm consists of a spectral initialization step followed by gradient descent. We provide extensive theoretical guarantees on our algorithm, showing that it converges quickly to the ground truth metric despite the non-convexity of the loss in our model. Because our focus is on fairness, we also show that individual fairness with respect to an estimated metric is sufficient to achieve similar fairness with respect to the true metric. We also discuss potential applications of our work to AI model tuning. Finally, we present experimental results that demonstrate the convergence of our algorithm and the fairness performance of downstream fair predictors trained on our estimated metric.