Modeling the interference effect is an important issue in the field of causal inference. Existing studies rely on explicit and often homogeneous assumptions regarding interference structures. In this paper, we introduce a low-rank and sparse treatment effect model that leverages data-driven techniques to identify the locations of interference effects. A profiling algorithm is proposed to estimate the model coefficients, and based on these estimates, global test and local detection methods are established to detect the existence of interference and the interference neighbor locations for each unit. We derive the non-asymptotic bound of the estimation error, and establish theoretical guarantees for the global test and the accuracy of the detection method in terms of Jaccard index. Simulations and real data examples are provided to demonstrate the usefulness of the proposed method.

翻译：在因果推断领域中，对干扰效应进行建模是一个重要问题。现有研究依赖于对干扰结构明确且通常同质化的假设。本文提出了一种低秩稀疏处理效应模型，该模型利用数据驱动技术识别干扰效应的位置。我们提出了一种剖析算法来估计模型系数，并基于这些估计建立了全局检验与局部检测方法，以检测每个单元是否存在干扰效应及其干扰邻域位置。我们推导了估计误差的非渐近界，并从Jaccard指数的角度为全局检验和检测方法的准确性建立了理论保证。通过仿真实验和实际数据案例验证了所提方法的实用性。