DCD: Decomposition-based Causal Discovery from Autocorrelated and Non-Stationary Temporal Data

The widespread availability of complex time series data in various domains such as environmental science, epidemiology, and economics demands robust causal discovery methods that can identify intricate contemporaneous and lagged relationships in non-stationary, nonlinear, and noisy settings. Existing constraint-based methods often rely heavily on conditional independence tests that degrade for limited data samples and complex distributions, while score-based methods impose strong statistical assumptions. Recent methods address special cases such as change point detection or distribution shifts, but struggle to provide a unified solution. We propose the Transformer Integrated Temporal Causal Discovery (TTCD) Framework, a novel end-to-end approach that learns contemporaneous and lagged causal relations from non-stationary time series. TTCD introduces a Non-Stationary Feature Learner integrating temporal and frequency-domain attention with dynamic non-stationarity profiling, and a custom Causal Structure Learner. A key innovation is reconstruction-guided causal signal distillation, to distill essential causal signals through the reconstruction process of the transformer decoder, which mitigates noise and spurious correlations while preserving meaningful dependencies. The Causal Structure Learner operates on distilled reconstructed signals to infer the underlying causal graph without restrictive assumptions on noise distributions or data generation processes. Experiments on synthetic, benchmark, and real world datasets show that TTCD consistently outperforms state-of-the-art baselines in both accuracy and consistency with domain knowledge, demonstrating the approach's effectiveness for causal discovery in challenging real world contexts.

Causal discovery in multivariate time series data is challenging due to complex interactions, high dimensionality, and nonlinear dependencies among variables. Existing methods often struggle to capture these complexities, resulting in inaccurate causal structures. To address this issue, we propose a novel framework that leverages self-attention mechanisms within the transformer architecture for causal discovery. Our approach introduces a novel inverted causal self-attention mechanism (CSAM) that emphasizes latent and indirect causal relationships by inverting tokens and inducing sparsity in attention scores, focusing on significant causal interactions and reducing spurious correlations. Additionally, we develop a global causal algorithm to identify global causal links, providing a holistic metric for causal influence, along with a causal verification module to ensure robustness in the identified causal relationships, enhancing the reliability of our framework. Experiments on both linear and nonlinear datasets, along with ablation studies and sensitivity analyses, show that our framework outperforms existing methods, demonstrating its potential for causal discovery in complex multivariate time series.

Causal discovery with instantaneous effects in multivariate time series is challenging, as the instantaneous structure must be acyclic. Prior methods enforce this by either separating instantaneous and lagged estimation into multi-stage pipelines or imposing algebraic acyclicity constraints via complex augmented Lagrangian optimization, both of which incur high computational cost. In this work, we propose a different approach: we learn a differentiable permutation of variables using the Gumbel--Sinkhorn operator and triangularize the instantaneous coefficient matrix of a Structural Vector Autoregressive (SVAR) model in the learned order. This converts acyclicity from a hard constraint into a parameterization and keeps it valid throughout optimization. In doing so, our method enables unified, continuous optimization with gradient-based learning, leading to improved efficiency in time--series causal discovery. Across three real-world benchmarks, our method achieves the best overall performance compared with 12 baselines in both discovery accuracy and efficiency. On the large-scale benchmark, it further demonstrates strong scalability, achieving more than a 6x speedup over competing methods.