DVAE: A Dynamic Variational Autoencoder for Structured Causal Discovery with Application in Biomedical Time Series

Causal discovery in time-series data is critical for analyzing dynamic systems across neuroscience, economics, and biomedical signal processing. Traditional methods, such as Vector Auto-regression (VAR) and constraint-based approaches, struggle with high-dimensional dependencies, nonlinear relationships, and non-stationary dynamics. Deep learning-based models, including cMLP, cLSTM, and VAE-based approaches, aim to address these challenges but suffer from instability, over-pruning, and reliance on sparsity constraints. While cMLP provides lag-specific causal inference, its accuracy is limited, and other methods fail to explicitly capture lag-wise dependencies. This paper introduces DVAE-GC, a structured deep learning framework integrating dynamic variational inference with lag-structured recurrent MLPs (lsrMLP) to explicitly model time-lagged causal dependencies. Unlike prior methods that infer causality via weight sparsity, DVAE-GC progressively refines causal estimation, leveraging a bidirectional recurrent encoder and structured decoder. Additionally, Noise Invalidation Soft Thresholding (NIST) eliminates spurious connections, enhancing interpretability and robustness. Empirically, DVAE-GC outperforms the best baseline (CUTS) on VAR(9) by +18.3 absolute F1 points averaged over multiple noise levels, and on NetSim fMRI-20 by +8.1 absolute F1 points averaged over sequence multiple lengths; in simulated atrial rotor detection, it improves Rotational Activity Estimation Precision (RAEP) by +22.4 % over the best alternative (VAR). These are absolute-point gains, and also precision, recall, and false discovery rate (FDR) has been reported. Although evaluated in biomedical simulations, DVAE-GC applies broadly to time-series domains, including neuroscience, climate science, and financial modeling.