新方法A-IHF搞定了工具变量残差提取
A-IHF (Adaptive Anisotropic Instrumental Heat Flow) 是一种用于控制函数工具变量估计的确定性图扩散残差提取方法。它利用图结构对处理变量进行各向异性扩散，通过检测处理值的大跳跃并衰减跨跳跃的导纳，生成稀疏图求解的残差。在包含图、核、树、提升、级联和神经网络等控制函数基线的54个合成基准单元中，受保护观测型A-IHF取得了最低的平均结构响应均方误差（MSE），并在32个单元中优于最佳非A-IHF基线。
Graph Diffusion Residuals for Control-Function Instrumental Variables
Control-function instrumental variable estimators need a first-stage residual, not merely a first-stage prediction. High-capacity first stages can interpolate treatment and leave too little residual information for the outcome equation. We study Adaptive Anisotropic Instrumental Heat Flow (A-IHF), a deterministic graph-diffusion residual extractor for flexible control functions. A-IHF treats treatment as a signal on a graph of first-stage features, uses pilot diffusion to detect large treatment jumps, attenuates conductance across those jumps, and computes the generated control with a sparse graph resolvent. Its observational selection rule uses only $(Z,X)$, combining graph generalized cross-validation, roughness, residualized-treatment relevance, and graph-admissibility filtering. The analysis decomposes error into structural leakage, residual attenuation, and residualized treatment variation, yielding finite-sample bounds, graph-admissibility rates under latent piecewise-smooth geometry, and finite-path selection calibration. Across 54 synthetic benchmark cells with tuned graph, kernel, tree, boosting, series, and neural control-function baselines, guarded observational A-IHF has the lowest average structural-response MSE; the A-IHF family beats the best non-A-IHF baseline in 32 cells. Performance is strongest when the graph captures piecewise-smooth first-stage structure.