The project aims to incorporate the reliable uncertainty estimate from Gaussian Processes (GP) into causality inference. Recent work on causality inference based on kernel methods have demonstrated both theoretical guarantees and good empirical performances. Therefore, the aim of this project to extend from kernel methods to Gaussian Processes is natural, and furthermore, Gaussian Processes can provide a principled quantification of uncertainty, which is also useful in improving causality inference performance by rejecting the prediction with low confidence. Considering the computational complexity of Gaussian Process inference, it might require approximation techniques like variational approximations to improve the scalability of this approach.