Nonlinear Causal Discovery in Time Series

Tianhao Wu, Xingyu Wu, Xin Wang, Shikang Liu, Huanhuan Chen

Abstract: Recent years have witnessed the proliferation of the Functional Causal Model (FCM) for causal learning due to its intuitive representation and accurate learning results. However, existing FCM-based algorithms suffer from the ubiquitous nonlinear relations in time-series data, mainly because these algorithms either assume linear relationships, or nonlinear relationships with additive noise, or do not introduce additional assumptions but can only identify nonlinear causality between two variables. This paper contributes in particular to a practical FCM-based causal learning approach, which can maintain effectiveness for real-world nonstationary data with general nonlinear relationships and unlimited variable scale.Specifically, the non-stationarity of time series data is first exploited with the nonlinear independent component analysis, to discover the underlying components or latent disturbances. Then, the conditional independence between variables and these components is studied to obtain a relation matrix, which guides the algorithm to recover the underlying causal graph. The correctness of the proposal is theoretically proved, and extensive experiments further verify its effectiveness. To the best of our knowledge, the proposal is the first so far that can fully identify causal relationships under general nonlinear conditions.