def test_multi_scale_inducing_equivalence_inducing_points(N, M, D):
# Multiscale must be equivalent to inducing points when variance is zero
Xnew, Z = np.random.randn(N, D), np.random.randn(M, D)
rbf = gpflow.kernels.SquaredExponential(1.3441,
lengthscale=np.random.uniform(
0.5, 3., D))
inducing_variable_zero_lengthscale = Multiscale(Z,
scales=np.zeros(Z.shape))
inducing_variable_inducing_point = InducingPoints(Z)
multi_scale_Kuf = Kuf(inducing_variable_zero_lengthscale, rbf, Xnew)
inducing_point_Kuf = Kuf(inducing_variable_inducing_point, rbf, Xnew)
deviation_percent_Kuf = np.max(
np.abs(multi_scale_Kuf - inducing_point_Kuf) / inducing_point_Kuf *
100)
assert deviation_percent_Kuf < 0.1
multi_scale_Kuu = Kuu(inducing_variable_zero_lengthscale, rbf)
inducing_point_Kuu = Kuu(inducing_variable_inducing_point, rbf)
deviation_percent_Kuu = np.max(
np.abs(multi_scale_Kuu - inducing_point_Kuu) / inducing_point_Kuu *
100)
assert deviation_percent_Kuu < 0.1
def test_multi_scale_inducing_equivalence_inducing_points(N, M, D):
# Multiscale must be equivalent to inducing points when variance is zero
Xnew, Z = np.random.randn(N, D), np.random.randn(M, D)
rbf = gpflow.kernels.SquaredExponential(1.3441,
lengthscales=np.random.uniform(
0.5, 3.0, D))
inducing_variable_zero_lengthscales = Multiscale(Z,
scales=np.zeros(Z.shape) +
1e-10)
inducing_variable_inducing_point = InducingPoints(Z)
multi_scale_Kuf = Kuf(inducing_variable_zero_lengthscales, rbf, Xnew)
inducing_point_Kuf = Kuf(inducing_variable_inducing_point, rbf, Xnew)
relative_error_Kuf = np.abs(multi_scale_Kuf -
inducing_point_Kuf) / inducing_point_Kuf
assert np.max(relative_error_Kuf) < 0.1e-2 # 0.1 %
multi_scale_Kuu = Kuu(inducing_variable_zero_lengthscales, rbf)
inducing_point_Kuu = Kuu(inducing_variable_inducing_point, rbf)
relative_error_Kuu = np.abs(multi_scale_Kuu -
inducing_point_Kuu) / inducing_point_Kuu
assert np.max(relative_error_Kuu) < 0.1e-2 # 0.1 %
[
2,
InducingPoints(np.random.randn(71, 2)),
gpflow.kernels.SquaredExponential(variance=1.84,
lengthscales=np.random.uniform(
0.5, 3.0, 2)),
],
[
2,
InducingPoints(np.random.randn(71, 2)),
gpflow.kernels.Matern12(variance=1.84,
lengthscales=np.random.uniform(0.5, 3.0, 2)),
],
[
2,
Multiscale(np.random.randn(71, 2),
np.random.uniform(0.5, 3, size=(71, 2))),
gpflow.kernels.SquaredExponential(variance=1.84,
lengthscales=np.random.uniform(
0.5, 3.0, 2)),
],
[
9,
InducingPatches(np.random.randn(71, 4)),
gpflow.kernels.Convolutional(gpflow.kernels.SquaredExponential(),
[3, 3], [2, 2]),
],
]
@pytest.mark.parametrize("input_dim, inducing_variable, kernel",
_inducing_variables_and_kernels)