https://github.com/GPflow/GPflow
Tip revision: 5a08eb80e36aa90e29077ad042a60d1bce6470ae authored by Artem Artemev on 21 June 2019, 10:40:38 UTC
Custom squared distances gradients
Custom squared distances gradients
Tip revision: 5a08eb8
test_features.py
# Copyright 2017 Mark van der Wilk
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
from numpy.testing import assert_allclose, assert_equal
import pytest
import gpflow
from gpflow.features import InducingPoints, Multiscale
from gpflow.covariances import Kuu, Kuf
from gpflow.config import default_jitter
@pytest.mark.parametrize('N, D', [[17, 3], [10, 7]])
def test_inducing_points_feature_len(N, D):
Z = np.random.randn(N, D)
features = InducingPoints(Z)
assert_equal(len(features), N)
_kernel_setups = [
gpflow.kernels.RBF(variance=0.46,
lengthscale=np.random.uniform(0.5, 3., 5),
ard=True),
gpflow.kernels.Periodic(period=0.4, variance=1.8)
]
@pytest.mark.parametrize('N', [10, 101])
@pytest.mark.parametrize('kernel', _kernel_setups)
def test_inducing_equivalence(N, kernel):
# Inducing features must be the same as the kernel evaluations
Z = np.random.randn(N, 5)
features = InducingPoints(Z)
assert_allclose(Kuu(features, kernel), kernel(Z))
@pytest.mark.parametrize('N, M, D', [[23, 13, 3], [10, 5, 7]])
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.RBF(1.3441, lengthscale=np.random.uniform(0.5, 3., D))
feature_zero_lengthscale = Multiscale(Z, scales=np.zeros(Z.shape))
feature_inducing_point = InducingPoints(Z)
multi_scale_Kuf = Kuf(feature_zero_lengthscale, rbf, Xnew)
inducing_point_Kuf = Kuf(feature_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(feature_zero_lengthscale, rbf)
inducing_point_Kuu = Kuu(feature_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
_features_and_kernels = [
[
InducingPoints(np.random.randn(71, 2)),
gpflow.kernels.RBF(variance=1.84,
lengthscale=np.random.uniform(0.5, 3., 2))
],
[
InducingPoints(np.random.randn(71, 2)),
gpflow.kernels.Matern12(variance=1.84,
lengthscale=np.random.uniform(0.5, 3., 2))
],
[
Multiscale(np.random.randn(71, 2),
np.random.uniform(0.5, 3, size=(71, 2))),
gpflow.kernels.RBF(variance=1.84,
lengthscale=np.random.uniform(0.5, 3., 2))
]
]
@pytest.mark.parametrize('feature, kernel', _features_and_kernels)
def test_features_psd_schur(feature, kernel):
# Conditional variance must be PSD.
X = np.random.randn(5, 2)
Kuf_values = Kuf(feature, kernel, X)
Kuu_values = Kuu(feature, kernel, jitter=default_jitter())
Kff_values = kernel(X)
Qff_values = Kuf_values.numpy().T @ np.linalg.solve(Kuu_values, Kuf_values)
assert np.all(np.linalg.eig(Kff_values - Qff_values)[0] > 0.0)