GAHMN: A Generative Approach for High-Dimensional Mediation Analysis

High-dimensional mediation analysis (HMA) seeks to uncover complex causal mechanisms involving numerous mediators and plays a crucial role in scientific and social sciences. In this work, we introduce the Generative Adversarial High-dimensional Mediation Network (GAHMN), a novel, scalable structured generative framework designed for causal analysis in high-dimensional settings. GAHMN formulates mediation analysis as dual conditional generative blocks, explicitly capturing mediators' dual roles as outcomes influenced by treatments and as predictors affecting outcomes. Each block integrates a high-dimensional partially linear structure with multi-channel convolutional layers, promoting effective parameter sharing and enhanced representation learning. To induce sparsity and accurate mediator selection, GAHMN employs customized min-max optimization problems with L1 penalties on generator parameters, alongside specially designed optimization algorithms for efficient computation. Unlike existing benchmark methods relying on restrictive parametric assumptions or random-effect specifications, GAHMN flexibly captures heterogeneity, complex distributions, and inter-mediator correlations. With careful design, the computational complexity of GAHMN scales linearly with the number of mediators p, rather than quadratically as in conventional approaches. Theoretical results rigorously ensures estimation consistency, convergence rate, and accurate sparse recovery. GAHMN also serves as a structured generative causal modeling framework, extending to causal decomposition, structural equation modeling, and counterfactual policy evaluation. Extensive experiments confirm GAHMN's superior performance and robustness in synthetic and real-world scenarios.