def kernel_periodic(matrix_1, matrix_2, parameters):
p = parameters[0]
l = parameters[1]
matrix = norm_matrix(matrix_1, matrix_2)
K = np.exp(-np.sin(matrix * np.pi / p)**2 / l**2)
return K
def kernel_gaussian_linear(matrix_1, matrix_2, parameters):
K = 0
matrix = norm_matrix(matrix_1, matrix_2)
for i in range(parameters.shape[1]):
# print("beta", parameters[1, i])
# print("sigma", parameters[0, i])
K = K + parameters[1, i]**2 * np.exp(-matrix /
(2 * parameters[0, i]**2))
return K
def kernel_bernoulli(matrix_1, matrix_2, parameters):
matrix = norm_matrix(matrix_1, matrix_2)
alpha_0 = parameters[0]
sigma_0 = parameters[1]
alpha_1 = parameters[2]
sigma_1 = parameters[3]
K = alpha_0 * np.maximum(0, 1 - matrix /
(sigma_0)) + alpha_1 * np.exp(-matrix /
(2 * sigma_1**2))
return K
def kernel_rational_quadratic_gaussian(matrix_1, matrix_2, parameters):
alpha = parameters[0]
beta = parameters[1]
sigma = parameters[2]
delta_1 = parameters[3]
delta_2 = parameters[4]
c = parameters[5]
matrix = norm_matrix(matrix_1, matrix_2)
K = c + delta_1**2 * (
(beta**2 + matrix)**(-(alpha))) + delta_2**2 * np.exp(-matrix /
(2 * sigma**2))
return K
def kernel_cauchy(matrix_1, matrix_2, parameters):
sigma = parameters[0]
matrix = norm_matrix(matrix_1, matrix_2)
return 1 / (1 + matrix / sigma**2)
def kernel_inverse_multiquad(matrix_1, matrix_2, parameters):
beta = parameters[0]
gamma = parameters[1]
matrix = norm_matrix(matrix_1, matrix_2)
return (beta**2 + gamma * matrix)**(-1 / 2)
def kernel_inverse_power_alpha(matrix_1, matrix_2, parameters):
alpha = parameters[0]
beta = 1.0
epsilon = 0.0001
matrix = norm_matrix(matrix_1, matrix_2)
return (beta**2 + matrix)**(-(alpha + epsilon))
def kernel_rational_quadratic(matrix_1, matrix_2, parameters):
alpha = parameters[0]
beta = parameters[1]
epsilon = 0.0001
matrix = norm_matrix(matrix_1, matrix_2)
return (beta**2 + matrix)**(-(alpha + epsilon))
def kernel_laplacian(matrix_1, matrix_2, parameters):
gamma = parameters[0]
matrix = np.sqrt(norm_matrix(matrix_1, matrix_2))
K = np.exp(-matrix * gamma)
return K
def kernel_RBF(matrix_1, matrix_2, parameters):
matrix = norm_matrix(matrix_1, matrix_2)
sigma = parameters[0]
K = np.exp(-matrix / (2 * sigma**2))
return K