Constraint- and Score-Based Nonlinear Granger Causality Discovery with Kernels
This work addresses the challenge of nonlinear causal discovery for time series analysis, offering incremental improvements in accuracy and efficiency.
The paper tackles the problem of identifying nonlinear causal relationships in time series by unifying two kernel-based Granger causality methods under a Kernel Principal Component Regression framework and introducing a Gaussian Process score-based model with Smooth Information Criterion penalisation, resulting in improved performance over state-of-the-art methods.
Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality (GC) approaches can be theoretically unified under the framework of Kernel Principal Component Regression (KPCR), and introduce a method based on this unification, demonstrating that this approach can improve causal identification. Additionally, we introduce a Gaussian Process score-based model with Smooth Information Criterion penalisation on the marginal likelihood, and demonstrate improved performance over existing state of the art time-series nonlinear causal discovery methods. Furthermore, we propose a contemporaneous causal identification algorithm, fully based on GC, using the proposed score-based $GP_{SIC}$ method, and compare its performance to a state of the art contemporaneous time series causal discovery algorithm.