We study causal effect estimation under interference from network data. We work under the chain-graph formulation pioneered in Tchetgen Tchetgen et. al (2021). Our first result shows that polynomial time evaluation of treatment effects is computationally hard in this framework without additional assumptions on the underlying chain graph. Subsequently, we assume that the interactions among the study units are governed either by (i) a dense graph or (ii) an i.i.d. Gaussian matrix. In each case, we show that the treatment effects have well-defined limits as the population size diverges to infinity. Additionally, we develop polynomial time algorithms to consistently evaluate the treatment effects in each case. Finally, we estimate the unknown parameters from the observed data using maximum pseudo-likelihood estimates, and establish the stability of our causal effect estimators under this perturbation. Our algorithms provably approximate the causal effects in polynomial time even in low-temperature regimes where the canonical MCMC samplers are slow mixing. For dense graphs, our results use the notion of regularity partitions; for Gaussian interactions, our approach uses ideas from spin glass theory and Approximate Message Passing.

翻译：本研究探讨基于网络数据的干扰条件下因果效应估计问题。我们采用Tchetgen Tchetgen等人（2021）开创的链图模型框架。首个理论结果表明，若不对底层链图施加额外假设，在该框架下多项式时间评估处理效应具有计算复杂性。随后我们假设研究单元间的交互作用遵循以下两种模式之一：（i）稠密图结构或（ii）独立同分布高斯矩阵。针对每种情形，我们证明当群体规模趋于无穷时，处理效应存在明确定义的极限。此外，我们分别开发了多项式时间算法以一致地评估两种情形下的处理效应。最后，我们通过最大伪似然估计从观测数据中估计未知参数，并证明了在此扰动下因果效应估计量的稳定性。即使在典型MCMC采样器混合速度缓慢的低温区域，我们的算法仍能在多项式时间内可证明地逼近因果效应。对于稠密图情形，我们的结果采用正则划分概念；对于高斯交互情形，我们的方法借鉴自旋玻璃理论与近似消息传递的思想。