TS-CausalNN: Learning Temporal Causal Relations from Non-linear
  Non-stationary Time Series Data
Omar Faruque Sahara Ali Xue Zheng Jianwu Wang
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.