Graph Diffusion Residuals for Control-Function Instrumental Variables
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Computer Science > Machine Learning
Title:Graph Diffusion Residuals for Control-Function Instrumental Variables
Abstract: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.
| Comments: | Submitted to Journal of Machine Learning Research (JMLR). 50 pages, 6 figures |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2606.14636 [cs.LG] |
| (or arXiv:2606.14636v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.14636
arXiv-issued DOI via DataCite (pending registration)
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