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# Causal Discovery for Non-stationary Non-linear Time Series Data Using Just-In-Time Modeling

*Proceedings of the Second Conference on Causal Learning and Reasoning*, PMLR 213:880-894, 2023.

#### Abstract

Causal discovery from multivariate continuous time-series data is becoming more important as the amount of IoT data to analyze increases. However, it is not easy to identify the causal structure from such data using conventional linear causal discovery methods due to their non-stationary characteristics such as distribution shifts, and non-linearity of the system dynamics. The application of non-linear causal discovery methods is also generally limited, and there are still some problems such as their computational complexity, interpretability, and robustness for non-stationarity. To address these challenges, we propose a new causal discovery method JIT-LiNGAM, based on the Linear Non-Gaussian Acyclic Model (LiNGAM) and the Just-In-Time (JIT) framework, which is also called Lazy-Learning or Model-On-Demand. Our method estimates a local linear structural causal model from neighboring samples of the past data every time a new input sample is given. Approximating an inherently globally non-linear model with local linear models, we can benefit from high detection performance of causal relationship for non-linear and non-stationary data, improvements of interpretability of causal effects by linear expression, and reduced computational complexity. We formulate this algorithm based on Taylor’s theorem, and show effective neighbor selection algorithms by a simple experiment. The results of numerical experiments using artificial data with non-linearity and non-stationarity demonstrate the effectiveness of our method compared to representative methods for such data, under some general evaluation metrics.