Randomized graph cluster randomization

Abstract The global average treatment effect (GATE) is a primary quantity of interest in the study causal inference under network interference. With correctly specified exposure model interference, Horvitz–Thompson (HT) and Hájek estimators GATE are unbiased consistent, respectively, yet known to exhibit extreme variance many designs settings interest. fixed clustering interference graph, graph cluster randomization (GCR) have been shown greatly reduce compared node-level random assignment, but even so still often prohibitively large. In this work, we propose randomized version GCR design, descriptively named (RGCR), which uses rather than single clustering. By considering an ensemble different assignments, design avoids key problem with where probability given node can be exponentially small We two inherently decomposition algorithms for use RGCR designs, 3-net 1-hop-max , adapted from prior work on multiway cut problems probabilistic approximation (graph) metrics. also weighted extensions these slight additional advantages. All result probabilities that estimated efficiently. derive structure-dependent upper bounds HT estimator GATE, depending metric structure driving Where best-known such bound exponential parameters structure, give comparable instead polynomial same parameters. provide extensive simulations comparing observing substantial improvements estimation variety settings.