Abstract
Convergent cross mapping (CCM) is designed for causal discovery in coupled time series, where Granger causality may not be applicable because of a separability assumption. However, CCM is not robust to observation noise which limits its applicability on signals that are known to be noisy. Moreover, the parameters for state space reconstruction need to be selected using grid search methods. In this paper, we propose a novel improved version of CCM using Gaussian processes for discovery of causality from noisy time series. Specifically, we adopt the concept of CCM and carry out the key steps using Gaussian processes within a non-parametric Bayesian probabilistic framework in a principled manner. The proposed approach is first validated on simulated data, and then used for understanding the interaction between fetal heart rate and uterine activity in the last two hours before delivery and of interest in obstetrics. Our results indicate that uterine activity affects the fetal heart rate, which agrees with recent clinical studies.