Causal effect estimation under network interference with mean-field methods
研究了观测数据中网络干扰下的因果效应估计，提出基于平均场和近似消息传递的可扩展算法，适用于密集交互场景，并证明了估计量的一致性。
We study causal effect estimation from observational data under interference. The interference pattern is captured by an observed network. We adopt the chain graph framework of (J. Amer. Statist. Assoc. 116 (2021) 833–844), which allows (i) interaction among the outcomes of distinct study units connected along the graph and (ii) long range interference, whereby the outcome of an unit may depend on the treatments assigned to distant units connected along the interference network. For “mean-field” interaction networks, we develop a new scalable iterative algorithm to estimate the causal effects. For Gaussian weighted networks, we introduce a novel causal effect estimation algorithm based on Approximate Message Passing (AMP). Our algorithms are provably consistent under a “high temperature” condition on the underlying model. We estimate the (unknown) parameters of the model from data using maximum pseudo-likelihood and establish n-consistency of this estimator in all parameter regimes. Finally, we prove that the downstream estimators obtained by plugging in estimated parameters into the aforementioned algorithms are consistent at high temperature. Our methods can accommodate dense interactions among the study units—a setting beyond reach using existing techniques. Our algorithms originate from the study of variational inference approaches in high-dimensional statistics; overall, we demonstrate the usefulness of these ideas in the context of causal effect estimation under interference.