Algorithm 2.

NoDFEs of Causal Modules P(Y |X)

1) Input: N observstions of X and Y.

2) Calculate Gram matrix $M_{\underset{\_}{Y}X}$ (see Eq. 3 for linear kernels and Eq. 4 for Gaussian kernels).

3) Find ${\widehat{\lambda }}_i(C)$ by directly feeding Gram matrix $M_{\underset{\_}{Y}X}$ to KPCA. That is, perform eigenvalue decomposition on M to find the nonlinear principal components ${\widehat{\lambda }}_i(C)$ [8].

4) Output: the estimation of nonstationary driving force ${\widehat{\lambda }}_i(C)$.