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Network interference, where the outcome of an individual is affected by thetreatment assignment of those in their social network, is pervasive inreal-world settings. However, it poses a challenge to estimating causaleffects. We consider the task of estimating the total treatment effect (TTE),or the difference between the average outcomes of the population when everyoneis treated versus when no one is, under network interference. Under a Bernoullirandomized design, we provide an unbiased estimator for the TTE when networkinterference effects are constrained to low order interactions among neighborsof an individual. We make no assumptions on the graph other than boundeddegree, allowing for well-connected networks that may not be easily clustered.We derive a bound on the variance of our estimator and show in simulatedexperiments that it performs well compared with standard estimators for theTTE. We also derive a minimax lower bound on the mean squared error of ourestimator which suggests that the difficulty of estimation can be characterizedby the degree of interactions in the potential outcomes model. We also provethat our estimator is asymptotically normal under boundedness conditions on thenetwork degree and potential outcomes model. Central to our contribution is anew framework for balancing model flexibility and statistical complexity ascaptured by this low order interactions structure.

Exploiting Neighborhood Interference with Low Order Interactions under Unit Randomized Design