Network interference occurs when treatments assigned to some units affect the outcomes of others. Traditional approaches often assume that the observed network correctly specifies the interference structure. However, in practice, researchers frequently only have access to proxy measurements of the interference network due to limitations in data collection or potential mismatches between measured networks and actual interference pathways. In this paper, we introduce a framework for estimating causal effects when only proxy networks are available. Our approach leverages a structural causal model that accommodates diverse proxy types, including noisy measurements, multiple data sources, and multilayer networks, and defines causal effects as interventions on population-level treatments. The latent nature of the true interference network poses significant challenges. To overcome them, we develop a Bayesian inference framework. We propose a Block Gibbs sampler with Locally Informed Proposals to update the latent network, thereby efficiently exploring the high-dimensional posterior space composed of both discrete and continuous parameters. The latent network updates are driven by information from the proxy networks, treatments, and outcomes. We illustrate the performance of our method through numerical experiments, demonstrating its accuracy in recovering causal effects even when only proxies of the interference network are available.

翻译：网络干扰发生在某些单元接受的处理影响其他单元结果时。传统方法通常假设观测网络能正确表征干扰结构。然而实践中，由于数据收集的局限性或测量网络与实际干扰路径间的潜在失配，研究者往往只能获得干扰网络的代理测量。本文提出了一种在仅可获得代理网络时估计因果效应的框架。我们的方法采用结构因果模型，该模型兼容多种代理类型（包括含噪测量、多数据源和多层网络），并将因果效应定义为对群体层面处理的干预。真实干扰网络的潜在特性带来了重大挑战。为克服这些挑战，我们开发了贝叶斯推断框架。我们提出具有局部信息提案的块吉布斯采样器来更新潜在网络，从而高效探索由离散和连续参数构成的高维后验空间。潜在网络的更新由代理网络、处理变量和结果变量的信息驱动。通过数值实验，我们展示了该方法在仅可获得干扰网络代理时仍能准确恢复因果效应的性能。