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

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. 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. The proposed model learns non-stationary features from input data through learning and aggregating nonlinear functions. Using these learned nonlinear features, the parallel custom causal convolution 2D layers learn causal connections between different variables. Through experiments on multiple synthetic and real world datasets, we demonstrate the effectiveness 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.