Interventional Deep Generative Models for Scalable Causal Discovery and Counterfactual Analysis

Abstract

Causal reasoning and “what-if” analysis allow us to predict the outcomes of hypothetical changes and are fundamental to decision support in high-stakes domains such as healthcare, economics, and robotics. Traditional causal-discovery methods can find cause-and-effect graphs under simple assumptions but struggle with large, complex datasets and cannot predict what might happen after a hypothetical change. Algorithms like PC, FCI, and NOTEARS reliably infer directed acyclic graphs (DAGs) under linear or simple nonlinear assumptions but fail to scale to high-dimensional data and lack mechanisms for counterfactual simulation. Conversely, deep generative models learn to reproduce complex data patterns but do not capture cause-and-effect relationships, so they cannot answer “what-if” questions. We propose Interventional Structural Deep Generative Models (IS-DGM), a unified framework that embeds a learnable DAG into the latent space of a variational autoencoder. We prove that, under realistic conditions, our approach can uniquely recover the true causal structure and generate reliable counterfactual predictions. IS-DGM enforces acyclicity via a continuous matrix-exponential penalty, encourages sparsity through 𝐿1 regularization, and introduces alatent-space intervention operator to clamp selected factors and propagate effects through the graph. Under mild exponential-family priors and with diverse interventional data, IS-DGM recovers the true DAG up to element-wise reparameterization. Empirically, on synthetic benchmarks (latent dimensions up to 100), IS-DGM reduces structural Hamming distance by 30–55% and achieves over 50% lower counterfactual RMSE than state-of-the-art baselines. On real clinical data (MIMIC-III), it halves prediction error of treatment-response simulations relative to identifiable VAEs and NOTEARS. Ablation studies confirm the necessity of each loss component, and scalability analyses quantify runtime and memory trade-offs. IS-DGM thus offers a principled, scalable solution for joint causal discovery and counterfactual inference in complex, high-dimensional settings.