C-iVAE: Causal Structure-Aware Identifiable VAE for Tabular Data with Limited Environments

Identifiable Variational Autoencoders (iVAEs) provide theoretical guarantees for decoupled representation learning, but their requirement for auxiliary environments grows linearly with latent dimension (O(dk)), which is often impractical in real-world scenarios. We propose the Causal Structure-Aware Identifiable Variational Autoencoder (C-iVAE), extending the identifiability framework to static tabular data domains where causal graphs are often known or partially accessible. By leveraging the hierarchical structure of directed acyclic graphs (DAGs), C-iVAE reduces computational demands to O(rk), where r ?l d denotes the number of root nodes. Our core hierarchical identifiability theory proves that non-root nodes can inherit sufficient variability from causal parents, eliminating the need for explicit environmental constraints. Beyond identifiability, C-iVAE's causally aware generation ensures learned representations naturally adhere to structural constraints, yielding logically consistent outputs and enhanced representational capacity. We employ a graph neural network encoder to learn asymmetric structural embeddings, distinguishing nodes sharing identical Markovian blankets. Experiments demonstrate C-iVAE's exceptional robustness in intervention generalization and DAG noise settings, achieving significant performance gains on real-world datasets. Code is available at https://github.com/shudiaoh/c-ivae.