Kernel modules

causalai.models.common.CI_tests.kernels

class causalai.models.common.CI_tests.kernels.KernelBase(**kargs)

__init__(**kargs)

static centered_kernel(K: ndarray) → ndarray

Remove data mean by returning HKH, where H=I-1/n In the linear setting where K=XX', simple linear algebra shows that HKH is essentially the kernel matrix (X-mu)(X-mu)' after centering the data matrix X, where each row is a sample. When using a non-linear kernel K, HKH centers the data in the kernel representation space.

abstract kernel(X: ndarray, Y: ndarray | None = None) → ndarray

Returns the nxn kernel matrix

kernel_matrix_regression(Kz: ndarray, epsilon: float = 1e-05) → ndarray

Closed form Kernel Matrix Regression for computing the regression coefficient A.K.A that predicts K using Kz. Here A = Kz^-1, we use epsilon to avoid degenerate cases. See slide 14 of https://members.cbio.mines-paristech.fr/~jvert/talks/070529asmda/asmda.pdf for explaination.

class causalai.models.common.CI_tests.kernels.LinearKernel

__init__()

kernel(X, Y=None)

Returns the nxn kernel matrix

class causalai.models.common.CI_tests.kernels.GaussianKernel(width='empirical')

__init__(width='empirical')

kernel(X, Y=None)

Returns the nxn kernel matrix