The Functional LiNGAM

We consider a causal order such as the cause and effect among variables. In the Linear Non-Gaussian Acyclic Model (LiNGAM), we can only identify the order if at least one of the variables is non-Gaussian. This paper extends the notion of variables to functions (Functional Linear Non-Gaussian Acyclic Model, Func-LiNGAM). We first prove that we can identify the order among random functions if and only if one of them is a non-Gaussian process. In the actual procedure, we approximate the functions by random vectors. To improve the correctness and efficiency, we propose to optimize the coordinates of the vectors in such a way as functional principal component analysis. The experiments contain an order identification simulation among multiple functions for given samples. In particular, we apply the Func-LiNGAM to recognize the brain connectivity pattern with fMRI data. We can see the improvements in accuracy and execution speed compared to existing methods.