Structural Equation-VAE: Disentangled Latent Representations for Tabular Data

Abstract: Learning interpretable latent representations from tabular data remains a challenge in deep generative modeling. We introduce SE-VAE (Structural Equation-Variational Autoencoder), a novel architecture that embeds measurement structure directly into the design of a variational autoencoder. Inspired by structural equation modeling, SE-VAE aligns latent subspaces with known indicator groupings and introduces a global nuisance latent to isolate construct-specific confounding variation. This modular architecture enables disentanglement through design rather than through statistical regularizers alone. We evaluate SE-VAE on a suite of simulated tabular datasets and benchmark its performance against a series of leading baselines using standard disentanglement metrics. SE-VAE consistently outperforms alternatives in factor recovery, interpretability, and robustness to nuisance variation. Ablation results reveal that architectural structure, rather than regularization strength, is the key driver of performance. SE-VAE offers a principled framework for white-box generative modeling in scientific and social domains where latent constructs are theory-driven and measurement validity is essential.