def residual_kernel_matrix_kernel_real(Kx, Z, num_eig, ARD=True):
"""K_X|Z"""
assert len(Kx) == len(Z)
assert num_eig <= len(Kx)
T = len(Kx)
D = Z.shape[1]
I = eye(T)
eig_Kx, eix = truncated_eigen(*eigdec(Kx, num_eig))
rbf = RBF(D, ARD=ARD)
white = White(D)
gp_model = GPR(Z, 2 * sqrt(T) * eix @ diag(sqrt(eig_Kx)) / sqrt(eig_Kx[0]),
rbf + white)
gpflow.train.ScipyOptimizer().minimize(gp_model)
sigma_squared = white.variance.value
Kz_x = rbf.compute_K_symm(Z)
P = I - Kz_x @ pdinv(Kz_x + sigma_squared * I)
return P @ Kx @ P.T
def regression_distance(Y: np.ndarray, Z: np.ndarray, ard=True):
"""d(z,z') = |f(z)-f(z')| where Y=f(Z) + noise and f ~ GP"""
import gpflow
from gpflow.kernels import White, RBF
from gpflow.models import GPR
n, dims = Z.shape
rbf = RBF(dims, ARD=ard)
rbf_white = rbf + White(dims)
gp_model = GPR(Z, Y, rbf_white)
gpflow.train.ScipyOptimizer().minimize(gp_model)
Kz_y = rbf.compute_K_symm(Z)
Ry = pdinv(rbf_white.compute_K_symm(Z))
Fy = Y.T @ Ry @ Kz_y # F(z)
M = Fy.T @ Fy
O = np.ones((n, 1))
N = O @ (np.diag(M)[:, None]).T
D = np.sqrt(N + N.T - 2 * M)
return D, Kz_y