We propose a new unified framework for causal inference when the counterfactual outcomes of interest depend on how agents are linked in a network. Such network interference describes a vast literature on spillovers, social interactions, social learning, information diffusion, social capital formation, and more. Our approach works by first characterizing how an agent is linked in the network using the configuration of other agents and connections nearby as measured by path distance. Counterfactual predictions are then made by pooling outcome data across similarly configured agents. In the paper, we introduce a new nonparametric regression function for causal inference with network interference, propose a k-nearest-neighbor estimator, and provide non-asymptotic bounds on mean squared error. We demonstrate our approach by estimating the causal impact of various network interventions on social capital formation in a many-networks experiment.

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