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Randomized experiments are widely used to estimate causal effects across many domains. However, classical causal inference approaches rely on independence assumptions that are violated by network interference, when the treatment of one individual influences the outcomes of others. All existing approaches require at least approximate knowledge of the network, which may be unavailable or costly to collect. We consider the task of estimating the total treatment effect (TTE), the average difference between the outcomes when the whole population is treated versus when the whole population is untreated. By leveraging a staggered rollout design, in which treatment is incrementally given to random subsets of individuals, we derive unbiased estimators for TTE that do not rely on any prior structural knowledge of the network, as long as the network interference effects are constrained to low-degree interactions among neighbors of an individual. We derive bounds on the variance of the estimators, and we show in experiments that our estimator performs well against baselines on simulated data. Central to our theoretical contribution is a connection between staggered rollout observations and polynomial extrapolation.
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Exploiting neighborhood interference with low-order interactions under unit randomized design
Abstract 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.
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- PAR ID:
- 10441795
- Date Published:
- Journal Name:
- Journal of Causal Inference
- Volume:
- 11
- Issue:
- 1
- ISSN:
- 2193-3685
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1515/jci-2022-0051
