FiSH: Fair Spatial Hotspots

TL;DR

This work introduces Fair Spatial Hot Spots (FiSH), a method to detect spatial hotspots under a fairness constraint defined by statistical parity across protected attributes, while preserving noteworthiness. The authors formalize the problem as a diverse, Pareto-efficient selection across the noteworthiness–fairness front, introducing the approximate tau-dpe task and a prefix-tree beam-search algorithm (FiSH) that efficiently navigates the combinatorial space of k-hotspot subsets. They propose evaluation metrics—Direct Comparison, Coverage, and Diversity—to quantify approximation quality relative to an exact tau-dpe solution, and validate FiSH on IHDS data, showing near-exact performance with orders-of-magnitude faster runtimes and solid scalability. The results demonstrate FiSH’s ability to produce high-quality, fair, and diverse hotspot sets suitable for policy action, with potential extensions to scored lists and user-driven trade-off preferences.

Abstract

Pervasiveness of tracking devices and enhanced availability of spatially located data has deepened interest in using them for various policy interventions, through computational data analysis tasks such as spatial hot spot detection. In this paper, we consider, for the first time to our best knowledge, fairness in detecting spatial hot spots. We motivate the need for ensuring fairness through statistical parity over the collective population covered across chosen hot spots. We then characterize the task of identifying a diverse set of solutions in the noteworthiness-fairness trade-off spectrum, to empower the user to choose a trade-off justified by the policy domain. Being a novel task formulation, we also develop a suite of evaluation metrics for fair hot spots, motivated by the need to evaluate pertinent aspects of the task. We illustrate the computational infeasibility of identifying fair hot spots using naive and/or direct approaches and devise a method, codenamed {\it FiSH}, for efficiently identifying high-quality, fair and diverse sets of spatial hot spots. FiSH traverses the tree-structured search space using heuristics that guide it towards identifying effective and fair sets of spatial hot spots. Through an extensive empirical analysis over a real-world dataset from the domain of human development, we illustrate that FiSH generates high-quality solutions at fast response times.

Figures (10)

• Figure 1: An illustration of hot spots of Low Educational Achievement in India
• Figure 2: Illustration of the N-F space with $k$-sized subsets of $\mathcal{S}$. The pareto frontier is marked with a dotted line. The circled points indicates a possible solution to the approximate $\tau$-dpe problem ($\tau = 4$). The exact $\tau$-dpe would comprise equally spaced points from the pareto frontier.
• Figure 3: FiSH's Search Tree: Nodes at level $k$ represent $k$ sized subsets of $\mathcal{S}$, and form points in the N-F space (Fig \ref{['fig:nfspace']}).
• Figure 4: Cov vs. m
• Figure 5: Cov vs. b,tau