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Primary Submission Category: Causal Inference in Networks

Estimating network-mediated causal effects via spectral embeddings

Authors: Alex Hayes, Keith Levin,

Presenting Author: Alex Hayes*

We develop a model for mediation in networks, where mediation occurs in a latent node embedding space. Under our model, nodal interventions have causal effects on nodal outcomes, and these effects can be partitioned into a direct effect independent of the network, and an indirect effect, which is induced by homophily. To estimate these network-mediated effects, we embed nodes into a low-dimensional Euclidean space via the adjacency spectral embedding. We then use the embeddings to fit two ordinary least squares models: (1) an outcome model that characterizes how nodal outcomes vary with nodal treatment, controls, and position in latent space; and (2) a mediator model that characterizes how latent positions vary with nodal treatment and controls. We prove that the estimated coefficients are asymptotically normal about the true coefficients under a sub-gamma generalization of the random dot product graph, a widely-used latent space model. Further, we show that these coefficients can be used in product-of-coefficients estimators for causal inference. Our method is easy to implement, scales to networks with millions of edges, and accommodates a wide variety of structured data.