def test_two_white_noises_unity_matrix_correlated(self):
level1 = 1
level2 = 2
inter = 0.5
matrix = np.array([[1, 0], [inter, 1]])
n1 = 3
n2 = 5
k1 = WhiteKernel(noise_level=level1, noise_level_bounds='fixed')
k2 = WhiteKernel(noise_level=level2, noise_level_bounds='fixed')
msk = MultiStateKernel((
k1,
k2,
), matrix, [matrix] * 2)
X = np.block([[np.zeros(n1), np.ones(n2)],
[np.arange(n1), np.arange(n2)]]).T
call_result = msk(X)
expected_result = np.diag(np.r_[np.full(n1, level1),
np.full(n2, level2 + inter**2)])
expected_result[np.arange(n1) + n1,
np.arange(n1)] = np.full(n1, inter * level1)
expected_result[np.arange(n1),
np.arange(n1) + n1] = np.full(n1, inter * level1)
self.assertAllClose(call_result, expected_result)
def test_multistate_kernel_for_independent_ar_kernels(self):
k1 = Matern(nu=0.5, length_scale=1.0, length_scale_bounds=(0.01, 100))
k2 = Matern(nu=0.5, length_scale=1.0, length_scale_bounds=(0.01, 100))
gpr_k1 = GaussianProcessRegressor(kernel=1.0*k1, random_state=0)
gpr_k2 = GaussianProcessRegressor(kernel=1.0*k2, random_state=0)
gpr_k1.fit(self.x1, self.y1)
gpr_k2.fit(self.x1, self.y2)
expected_length_scale = -1.0/math.log(0.5)
expected_constant = 1.25
params_k1 = gpr_k1.kernel_.get_params()
params_k2 = gpr_k2.kernel_.get_params()
self.assertAlmostEqual(params_k1['k2__length_scale'], expected_length_scale, delta=0.1)
self.assertAlmostEqual(params_k2['k2__length_scale'], expected_length_scale, delta=0.1)
self.assertAlmostEqual(params_k1['k1__constant_value'], expected_constant, delta=0.1)
self.assertAlmostEqual(params_k2['k1__constant_value'], expected_constant, delta=0.1)
ms_kernel = MultiStateKernel((k1, k2,), np.array([[1,0],[-0.5,1]]), [np.array([[0.0,0.0],[0.0,0.0]]), np.array([[2.0,2.0],[2.0,2.0]])])
gpr_msk = GaussianProcessRegressor(kernel=ms_kernel, random_state=0)
gpr_msk.fit(self.x, self.y)
params_msk=gpr_msk.kernel_.get_params()
self.assertAlmostEqual(params_msk['s0__length_scale'], expected_length_scale, delta=0.1)
self.assertAlmostEqual(params_msk['s1__length_scale'], expected_length_scale, delta=0.1)
assert_allclose(
params_msk['scale'],
np.array([[expected_constant**0.5, 0.0], [0.0,expected_constant**0.5]]),
1e-1
)
def test_two_white_noises_unity_matrix(self):
level1 = 1
level2 = 2
matrix = np.eye(2)
n1 = 3
n2 = 5
k1 = WhiteKernel(noise_level=level1, noise_level_bounds='fixed')
k2 = WhiteKernel(noise_level=level2, noise_level_bounds='fixed')
msk = MultiStateKernel((
k1,
k2,
), matrix, [matrix] * 2)
X = np.block([[np.zeros(n1), np.ones(n2)],
[np.arange(n1), np.arange(n2)]]).T
call_result, call_grad = msk(X, None, True)
expected_result = np.diag(np.r_[np.full(n1, level1),
np.full(n2, level2)])
expected_grad = np.zeros(shape=(n1 + n2, n1 + n2, 3))
expected_grad[np.arange(n1), np.arange(n1),
0] = np.full(n1, level1 * 2)
expected_grad[n1 + np.arange(n2), n1 + np.arange(n2),
2] = np.full(n2, level2 * 2)
expected_grad[np.arange(n1) + n1, np.arange(n1),
1] = np.full(n1, level1)
expected_grad[np.arange(n1), np.arange(n1) + n1,
1] = np.full(n1, level1)
self.assertAllClose(call_result, expected_result)
self.assertAllClose(call_grad, expected_grad)
def test_multistate_kernel_for_independent_white_kernels(self):
k1 = WhiteKernel(noise_level=1, noise_level_bounds='fixed')
k2 = WhiteKernel(noise_level=1, noise_level_bounds='fixed')
ms_kernel = MultiStateKernel((k1, k2,), np.array([[1,0],[-0.5,1]]), [np.array([[0.0,0.0],[0.0,0.0]]), np.array([[2.0,2.0],[2.0,2.0]])])
gpr_msk = GaussianProcessRegressor(kernel=ms_kernel, random_state=0)
gpr_msk.fit(self.x, self.y)
assert_allclose(gpr_msk.kernel_.theta, np.array([1.0, 0.0, 1.0]), 1e-1)
def test_multistate_sample_for_mixed_kernels(self):
k1 = Matern(nu=0.5, length_scale=1.0, length_scale_bounds=(0.01, 100))
k2 = WhiteKernel(noise_level=1, noise_level_bounds='fixed')
ms_kernel = MultiStateKernel((k1, k2,), np.array([[1,0],[-0.5,1]]), [np.array([[-2.0,-2.0],[-2.0,-2.0]]), np.array([[2.0,2.0],[2.0,2.0]])])
gpr_msk = GaussianProcessRegressor(kernel=ms_kernel, random_state=0)
gpr_msk.fit(self.x, self.y)
y_samples = gpr_msk.sample_y(self.x, random_state=0)
gpr_msk2 = GaussianProcessRegressor(kernel=ms_kernel, random_state=0)
gpr_msk2.fit(self.x, y_samples.reshape(-1))
assert_allclose(gpr_msk.kernel_.theta, gpr_msk2.kernel_.theta, 1e-1)
def test_multistate_predict_for_mixed_kernels(self):
k1 = Matern(nu=0.5, length_scale=1.0, length_scale_bounds=(0.01, 100))
k2 = WhiteKernel(noise_level=1, noise_level_bounds='fixed')
ms_kernel = MultiStateKernel((k1, k2,), np.array([[1,0],[-0.5,1]]), [np.array([[-2.0,-2.0],[-2.0,-2.0]]), np.array([[2.0,2.0],[2.0,2.0]])])
gpr_msk = GaussianProcessRegressor(kernel=ms_kernel, random_state=0)
gpr_msk.fit(self.x, self.y)
x1 = np.linspace(0.25 * self.sample_length, 0.75 * self.sample_length, num=self.sample_length).reshape(-1, 1)
x = np.block([[np.zeros_like(x1), x1], [np.ones_like(x1), x1]])
mean = gpr_msk.predict(x)
mean1 = mean[:self.sample_length]
mean2 = mean[self.sample_length:]
assert_allclose(mean1, -mean2, 1e-1)
def test_multistate_kernel_for_dependent_kernels(self):
k1 = WhiteKernel(noise_level=1, noise_level_bounds='fixed')
k2 = WhiteKernel(noise_level=1, noise_level_bounds='fixed')
ms_kernel = MultiStateKernel((
k1,
k2,
), np.array([[1, 0], [-0.5, 1]]), [
np.array([[0.0, 0.0], [0.0, 0.0]]),
np.array([[2.0, 2.0], [2.0, 2.0]])
])
gpr_msk = GaussianProcessRegressor(kernel=ms_kernel, random_state=0)
gpr_msk.fit(self.x, self.y)
self.assertAllClose(gpr_msk.kernel_.get_params()['scale'],
np.array([[1.0, 0.0], [1.0, 1.0]]), 1e-1)