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Estimating causal effects under interference is pertinent to many real-world settings. However, the true interference network may be unknown to the practitioner, precluding many existing techniques that leverage this information. A recent line of work with low-order potential outcomes models uses staggered rollout designs to obtain unbiased estimators that require no network information. However, their use of polynomial extrapolation can lead to prohibitively high variance. To address this, we propose a two-stage experimental design that restricts treatment rollout to a sub-population. We analyze the bias and variance of an interpolation-style estimator under this experimental design. Through numerical simulations, we explore the trade-off between the error attributable to the subsampling of our experimental design and the extrapolation of the estimator. Under low-order interactions models with degree greater than 1, the proposed design greatly reduces the error of the polynomial interpolation estimator, such that it outperforms baseline estimators, especially when the treatment probability is small., Comment: 30 pages, 13 figures

Network interference, where the outcome of an individual is affected by the treatment assignment of those in their social network, is pervasive in real-world settings. However, it poses a challenge to estimating causal effects. We consider the task of estimating the total treatment effect (TTE), or the difference between the average outcomes of the population when everyone is treated versus when no one is, under network interference. Under a Bernoulli randomized design, we provide an unbiased estimator for the TTE when network interference effects are constrained to low order interactions among neighbors of an individual. We make no assumptions on the graph other than bounded degree, allowing for well-connected networks that may not be easily clustered. We derive a bound on the variance of our estimator and show in simulated experiments that it performs well compared with standard estimators for the TTE. We also derive a minimax lower bound on the mean squared error of our estimator which suggests that the difficulty of estimation can be characterized by the degree of interactions in the potential outcomes model. We also prove that our estimator is asymptotically normal under boundedness conditions on the network degree and potential outcomes model. Central to our contribution is a new framework for balancing model flexibility and statistical complexity as captured by this low order interactions structure., Comment: 42 pages including citations and appendix, 2 figures (total of 12 subfigures)