High-Dimensional Detection of Spatial Interference Effects

Modeling interference effects in high-dimensional settings presents significant challenges due to the complexity of underlying dependence structures. Existing approaches often rely on explicit and homogeneous assumptions, limiting their applicability in real-world scenarios. In this paper, we introduce a novel low-rank and sparse treatment effect model that leverages high-dimensional techniques to identify interference structures without restrictive parametric assumptions. We propose an efficient profiling algorithm for estimating model coefficients and develop statistical methodologies for both global testing of interference existence and local detection of interference-affected units. Theoretical guarantees are established, including non-asymptotic error bounds for estimation and accuracy guarantees for detection based on the Jaccard index. Through numerical experiments, we demonstrate the effectiveness of our method in high-dimensional settings, highlighting its advantages in capturing complex interference patterns.