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
import tensorflow as tf

import gpflow
from gpflow.test_util import GPflowTestCase


class TestInducingPoints(GPflowTestCase):
    def test_feature_len(self):
        with self.test_context():
            N, D = 17, 3
            Z = np.random.randn(N, D)
            f = gpflow.features.InducingPoints(Z)

            self.assertTrue(len(f), N)
            with gpflow.params_as_tensors_for(f):
                self.assertTrue(len(f), N)
                # GPflow does not support re-assignment with different shapes at the moment

    def test_inducing_points_equivalence(self):
        # Inducing features must be the same as the kernel evaluations
        with self.test_context() as session:
            Z = np.random.randn(101, 3)
            f = gpflow.features.InducingPoints(Z)

            kernels = [
                gpflow.kernels.RBF(3, 0.46, lengthscales=np.array([0.143, 1.84, 2.0]), ARD=True),
                gpflow.kernels.Periodic(3, 0.4, 1.8)
            ]

            for k in kernels:
                self.assertTrue(np.allclose(session.run(f.Kuu(k)), k.compute_K_symm(Z)))


class TestMultiScaleInducing(GPflowTestCase):
    def prepare(self):
        rbf = gpflow.kernels.RBF(2, 1.3441, lengthscales=np.array([0.3414, 1.234]))
        Z = np.random.randn(23, 3)
        feature_0lengthscale = gpflow.features.Multiscale(Z, np.zeros(Z.shape))
        feature_inducingpoint = gpflow.features.InducingPoints(Z)
        return rbf, feature_0lengthscale, feature_inducingpoint

    def test_equivalence_inducing_points(self):
        # Multiscale must be equivalent to inducing points when variance is zero
        with self.test_context() as session:
            rbf, feature_0lengthscale, feature_inducingpoint = self.prepare()
            Xnew = np.random.randn(13, 3)

            ms, point = session.run([feature_0lengthscale.Kuf(rbf, Xnew), feature_inducingpoint.Kuf(rbf, Xnew)])
            pd = np.max(np.abs(ms - point) / point * 100)
            self.assertTrue(pd < 0.1)

            ms, point = session.run([feature_0lengthscale.Kuu(rbf), feature_inducingpoint.Kuu(rbf)])
            pd = np.max(np.abs(ms - point) / point * 100)
            self.assertTrue(pd < 0.1)


class TestFeaturesPsdSchur(GPflowTestCase):
    def test_matrix_psd(self):
        # Conditional variance must be PSD.
        X = np.random.randn(13, 2)

        def init_feat(feature):
            if feature is gpflow.features.InducingPoints:
                return feature(np.random.randn(71, 2))
            elif feature is gpflow.features.Multiscale:
                return feature(np.random.randn(71, 2), np.random.rand(71, 2))

        featkerns = [(gpflow.features.InducingPoints, gpflow.kernels.RBF),
                     (gpflow.features.InducingPoints, gpflow.kernels.Matern12),
                     (gpflow.features.Multiscale, gpflow.kernels.RBF)]
        for feat_class, kern_class in featkerns:
            with self.test_context() as session:
                # rbf, feature, feature_0lengthscale, feature_inducingpoint = self.prepare()
                kern = kern_class(2, 1.84, lengthscales=[0.143, 1.53])
                feature = init_feat(feat_class)
                Kuf, Kuu = session.run([feature.Kuf(kern, X), feature.Kuu(kern, jitter=gpflow.settings.jitter)])
                Kff = kern.compute_K_symm(X)
            Qff = Kuf.T @ np.linalg.solve(Kuu, Kuf)
            self.assertTrue(np.all(np.linalg.eig(Kff - Qff)[0] > 0.0))


if __name__ == "__main__":
    tf.test.main()