Balancing Interference and Correlation in Spatial Experimental Designs: A Causal Graph Cut Approach

This paper focuses on the design of spatial experiments to optimize the amount of information derived from the experimental data and enhance the accuracy of the resulting causal effect estimator. We propose a surrogate function for the mean squared error (MSE) of the estimator, which facilitates the use of classical graph cut algorithms to learn the optimal design. Our proposal offers three key advances: (1) it accommodates moderate to large spatial interference effects; (2) it adapts to different spatial covariance functions; (3) it is computationally efficient. Theoretical results and numerical experiments based on synthetic environments and a dispatch simulator that models a city-scale ridesharing market, further validate the effectiveness of our design. A python implementation of our method is available at https://github.com/Mamba413/CausalGraphCut.

To assess how a policy affects outcomes, we need to run randomized controlled trials or online experiments. However, when experiments take place across different locations, changes made in one area can influence nearby areas—a phenomenon called spatial interference. At the same time, observed outcomes may be spatially correlated (e.g., like weather patterns). Both interference and spatial correlation can challenge the estimation of the policy’s impact.Our work introduces the causal graph cut algorithm, a tool designed for experiments in scenarios where locations interfere with each other and are spatially connected. It handles both interference effects and adapts to different patterns of spatial connections. Additionally, the algorithm is efficient for analyzing large numbers of spatial regions, making it suitable for large-scale experiments across many locations. Using a city-level model—built with real data from a ridesharing company to realistically mimic driver and passenger behavior—we demonstrate that our method outperforms existing approaches.