Improving Convergent Cross Mapping for Causal Discovery with Gaussian Processes

Convergent cross mapping (CCM) is designed for causal discovery between coupled time series for which Granger's method for detecting causality is shown to be unreliable. The theoretical foundation of CCM is based on state space reconstruction, and therefore, for the accuracy of its results, the quality of the reconstruction is crucial. However, in the CCM framework, the reconstruction of an attractor manifold is usually implemented by direct delay embedding, where the reconstruction parameters are often selected by grid search methods. In this paper, we propose a more reliable and principled approach, which is based on Gaussian processes (GPs) that improves the attractor reconstruction. We validated the approach with the well-studied Lorenz attractor with and without observation noise. The experimental results indicate that our method is more robust to noise and that it consistently provides a reliable attractor manifold reconstruction. The proposed method was then tested on a real-world dataset, and the results suggested that the CCM equipped with an improved attractor manifold not only determined correctly the causal relationship but also improved the convergence, which is critical for causal discovery.