Optimal Design under Interference, Homophily, and Robustness Trade-offs
Vydhourie Thiyageswaran, Alex Kokot, Jennifer Brennan, Marina Meila, Christina Lee Yu, Maryam Fazel
TL;DR
The paper tackles estimating the global average treatment effect under network interference and homophily by formulating a potential-outcomes model that incorporates interference, homophily, and heterogeneous variation. It introduces a three-way trade-off framework parameterized by η (homophily), γ (interference), and κ (robustness) and targets worst-case MSE for the Horvitz–Thompson estimator, solving the design problem via a convex SDP with Gaussian rounding and an adapted Gram–Schmidt Walk. Theoretical guarantees demonstrate approximation bounds for the SDP-based method and explicit MSE bounds for the Gram–Schmidt Walk, with both approaches applicable to general similarity kernels beyond the graph Laplacian. Empirical results on synthetic networks and a village-network dataset show improvements over unit- and cluster-randomized designs, highlighting robust, scalable strategies for covariate balancing and interference-aware experimentation. Overall, the work provides principled tools for designing experiments that balance network interference, homophily, and robustness to heterogeneous variation in causal inference settings.
Abstract
To minimize the mean squared error (MSE) in global average treatment effect (GATE) estimation under network interference, a popular approach is to use a cluster-randomized design. However, in the presence of homophily, which is common in social networks, cluster randomization can instead increase the MSE. We develop a novel potential outcomes model that accounts for interference, homophily, and heterogeneous variation. In this setting, we establish a framework for optimizing designs for worst-case MSE under the Horvitz-Thompson estimator. This leads to an optimization problem over the covariance matrices of the treatment assignment, trading off interference, homophily, and robustness. We frame and solve this problem using two complementary approaches. The first involves formulating a semidefinite program (SDP) and employing Gaussian rounding, in the spirit of the Goemans-Williamson approximation algorithm for MAXCUT. The second is an adaptation of the Gram-Schmidt Walk, a vector-balancing algorithm which has recently received much attention. Finally, we evaluate the performance of our designs through various experiments on simulated network data and a real village network dataset.