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Balancing Interference and Correlation in Spatial Experimental Designs: A Causal Graph Cut Approach
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Proposes a causal graph cut algorithm that designs cluster-randomized spatial experiments by minimizing a surrogate of the DR estimator's MSE, solved with spectral graph cuts under spatial interference and correlation.
Problem
Designing spatial A/B experiments under spatial interference and outcome correlation to minimize the MSE of the average treatment effect estimator, which is NP-hard combinatorially.
Approach
A surrogate for the DR estimator's MSE that trades off an interference term (upper-bounded without cluster boundaries) against within-cluster residual correlation, so that the design reduces to a graph cut solvable by spectral clustering, adapting to the estimated covariance rather than using a minimax worst case.
Key results
- In the ridesharing simulator, the proposed ATE estimator achieves an MSE about 3.5 times smaller than the benchmark approaches.
- In synthetic environments, CGC achieves MSEs substantially smaller than CC, TNET and SC, and beats global and individual designs with 54% and 72% improvements.
- CGC closely matches the oracle OCGC that knows the true covariance matrix.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use causal graph cut instead of benchmark approaches | ATE estimation in the ridesharing simulator · Real-data-based simulator | MSE: 3.5 times lower | Helped |
| Use CGC instead of the global design | ATE estimation · Synthetic environments | relative MSE: 54% | Helped |
| Use CGC instead of the individual design | ATE estimation · Synthetic environments | relative MSE: 72% | Helped |
| Use CGC rather than the global design | ATE estimation · Real-data-based simulator | MSE | Helped |
| Use CGC rather than the individual design | ATE estimation · Real-data-based simulator | MSE | Helped |
| Use estimated covariance through the iterative framework instead of known covariance (ablation) | CGC · Synthetic environments | MSE | No clear effect |
| Fit outcome regression using pooled data across regions with longitude and latitude, rather than fitting each region separately (ablation) | CGC and OCGC · Synthetic environments | MSE | Helped |
| Use all collected datasets to refit the model rather than only the latest dataset (ablation) | CGC · Square spatial setting | MSE | Helped |
| Use a noised covariance matrix instead of the true covariance matrix (ablation) | OCGC · Single-experiment settings | MSE | No clear effect |
| Omit cross-fitting (ablation) | CGC · Synthetic and real-data-based experiments | MSE | No clear effect |
Surprising findings
- Global design is significantly less effective than individual design in the real-world simulator because of strong spatial correlation, while interference favors global designs.
Limitations
- Second-order interference term I2 is omitted from the surrogate objective, which may be non-negligible.
- Method primarily targets repeated independent experiments; single-experiment extension relies on prior covariance knowledge.
Experimental setup
Datasets: five-day historical ridesharing dataset (about 1 million observations for ML models) synthetic spatial grids
Benchmarks: synthetic spatial environments (square, rectangle, circle, fans) real-data-based ridesharing simulator (R=85 hexagonal regions)
Metrics: relative MSE of ATE estimator
Baselines: spectral clustering threeNet causal clustering global design individual design OCGC
Builds on: causal clustering doubly robust estimator for interference (Zhu et al.) spectral clustering cross-fitting
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