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.

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MOTIVATION: An important application of gene expression microarray data is the classification of samples into categories. Accurate classification depends upon the method used to identify the most relevant genes. Owing to the large number of genes and relatively small sample size, the selection process can be unstable. Modification of existing methods for achieving better analysis of microarray data is needed. RESULTS: We propose a Bayesian stochastic variable selection approach for gene selection based on a probit regression model with a generalized singular g-prior distribution for regression coefficients. Using simulation-based Markov chain Monte Carlo methods for simulating parameters from the posterior distribution, an efficient and dependable algorithm is implemented. It is also shown that this algorithm is robust to the choices of initial values, and produces posterior probabilities of related genes for biological interpretation. The performance of the proposed approach is compared with other popular methods in gene selection and classification via the well-known colon cancer and leukemia datasets in microarray literature. AVAILABILITY: A free Matlab code to perform gene selection is available at http://www.sta.cuhk.edu.hk/xysong/geneselection/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.