TS-CausalNN: Learning Temporal Causal Relations from Non-linear Non-stationary Time Series Data

TL;DR

TS-CausalNN tackles causal discovery in non-linear, non-stationary time series by introducing a parallel 2D causal convolutional architecture that learns both lagged and contemporaneous relations. It enforces acyclicity on the contemporaneous subgraph via an augmented Lagrangian objective, using $h(W^t)=\mathrm{tr}(e^{W^t \circ W^t})-n$ together with sparsity via $\lambda \|W\|_1$. The approach is validated on synthetic data and real-world turbulence and Arctic sea-ice datasets, demonstrating competitive or superior SHD, F1, and FDR relative to strong baselines, with ablations confirming the advantage of the 2D causal conv layers and robustness to noise and non-stationarity. The work advances practical causal graph learning for complex time series and provides a scalable, interpretable tool for domains where non-stationarity and nonlinearity are pervasive.

Abstract

The growing availability and importance of time series data across various domains, including environmental science, epidemiology, and economics, has led to an increasing need for time-series causal discovery methods that can identify the intricate relationships in the non-stationary, non-linear, and often noisy real world data. However, the majority of current time series causal discovery methods assume stationarity and linear relations in data, making them infeasible for the task. Further, the recent deep learning-based methods rely on the traditional causal structure learning approaches making them computationally expensive. In this paper, we propose a Time-Series Causal Neural Network (TS-CausalNN) - a deep learning technique to discover contemporaneous and lagged causal relations simultaneously. Our proposed architecture comprises (i) convolutional blocks comprising parallel custom causal layers, (ii) acyclicity constraint, and (iii) optimization techniques using the augmented Lagrangian approach. In addition to the simple parallel design, an advantage of the proposed model is that it naturally handles the non-stationarity and non-linearity of the data. Through experiments on multiple synthetic and real world datasets, we demonstrate the empirical proficiency of our proposed approach as compared to several state-of-the-art methods. The inferred graphs for the real world dataset are in good agreement with the domain understanding.

Figures (10)

• Figure 1: Temporal causal graph learned (right) from multivariate time series data (left) with causal links from the same and previous timesteps. Each node in the graph represents one variable at a specific timestep ( $t$ is present time and $t-i$ is a previous timestep). A directed edge denotes a causal relationship between cause and effect.
• Figure 2: Proposed TS-CausalNN model architecture to learn full temporal causal graph. The graph can be learned from the parallel Causal Conv2d layers.
• Figure 3: Proposed custom Causal Conv2D Layers.
• Figure 4: Causal graph of (a) our synthetic datasets and (b) the real world Turbulence Kinetic Energy (TKE) dataset.
• Figure 5: Comparison of ground truth summary causal graph with predicted graphs from DYNOTEARS and our proposed model for synthetic dataset 1.