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 Tchetgen Tchetgen et. al. (2021), 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 $\sqrt{n}$-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.

翻译：本研究探讨在干扰存在下从观测数据中估计因果效应的问题。干扰模式由观测网络所刻画。我们采用Tchetgen Tchetgen等人（2021）提出的链图框架，该框架允许：（i）沿网络连接的各个研究单元结果之间存在相互作用；（ii）长程干扰，即单元的结果可能依赖于沿干扰网络连接的远端单元所分配的处理。针对"均值场"交互网络，我们开发了一种新的可扩展迭代算法来估计因果效应。对于高斯加权网络，我们引入了一种基于近似消息传递（AMP）的新型因果效应估计算法。在基础模型满足"高温"条件时，我们的算法具有可证明的一致性。我们通过最大伪似然法从数据中估计模型的（未知）参数，并在所有参数范围内建立了该估计量的$\sqrt{n}$一致性。最后，我们证明了将通过估计参数代入上述算法得到的下游估计量在高温条件下具有一致性。我们的方法能够容纳研究单元之间的密集交互——这是现有技术无法处理的场景。这些算法源于对高维统计中变分推断方法的研究；总体而言，我们展示了这些思想在网络干扰下因果效应估计背景中的实用性。