_test_method_equivalence.py
``````# Copyright 2016 the GPflow authors.
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

import tensorflow as tf

import numpy as np
from numpy.testing import assert_allclose
from gpflow.config import default_jitter

import gpflow
from gpflow.test_util import GPflowTestCase

class TestEquivalence(GPflowTestCase):
"""
With a Gaussian likelihood, and inducing points (where appropriate)
positioned at the data, many of the gpflow methods are equivalent (perhaps
subject to some optimization).

Here, we make 5 models that should be the same, and make sure some
similarites hold. The models are:

1) GP Regression
2) Variational GP (with the likelihood set to Gaussian)
3) Sparse variational GP (likelihood is Gaussian, inducing points
at the data)
4) Sparse variational GP (as above, but with the whitening rotation
of the inducing variables)
5) Sparse variational GP Regression (as above, but there the inducing
variables are 'collapsed' out, as in Titsias 2009)
"""

def prepare(self):
rng = np.random.RandomState(0)
X = rng.rand(20, 1) * 10
Y = np.sin(X) + 0.9 * np.cos(X * 1.6) + rng.randn(*X.shape) * 0.8
Y = np.tile(Y, 2)  # two identical columns
self.Xtest = rng.rand(10, 1) * 10

m1 = gpflow.models.GPR(
X, Y, kernel=gpflow.kernels.SquaredExponential(1),
mean_function=gpflow.mean_functions.Constant())
m2 = gpflow.models.VGP(
X, Y, gpflow.kernels.SquaredExponential(1), likelihood=gpflow.likelihoods.Gaussian(),
mean_function=gpflow.mean_functions.Constant())
m3 = gpflow.models.SVGP(
X, Y, gpflow.kernels.SquaredExponential(1),
likelihood=gpflow.likelihoods.Gaussian(),
Z=X.copy(),
q_diag=False,
mean_function=gpflow.mean_functions.Constant())
m3.inducing_variables.trainable = False
m4 = gpflow.models.SVGP(
X, Y, gpflow.kernels.SquaredExponential(1),
likelihood=gpflow.likelihoods.Gaussian(),
Z=X.copy(), q_diag=False, whiten=True,
mean_function=gpflow.mean_functions.Constant())
m4.inducing_variables.trainable = False
m5 = gpflow.models.SGPR(
X, Y, gpflow.kernels.SquaredExponential(1),
Z=X.copy(),
mean_function=gpflow.mean_functions.Constant())

m5.inducing_variables.trainable = False
m6 = gpflow.models.GPRFITC(
X, Y, gpflow.kernels.SquaredExponential(1), Z=X.copy(),
mean_function=gpflow.mean_functions.Constant())
m6.inducing_variables.trainable = False
return [m1, m2, m3, m4, m5, m6]

def test_all(self):
with self.test_context() as session:
models = self.prepare()
likelihoods = []
for m in models:
opt = gpflow.train.ScipyOptimizer()
opt.minimize(m, maxiter=300)
neg_obj = tf.negative(m.objective)
likelihoods.append(session.run(neg_obj).squeeze())
assert_allclose(likelihoods, likelihoods[0], rtol=1e-6)
variances, lengthscale = [], []
for m in models:
if hasattr(m.kernel, 'rbf'):
else:
variances, lengthscale = np.array(variances), np.array(lengthscale)
assert_allclose(variances, variances[0], 1e-5)
assert_allclose(lengthscale, lengthscale.mean(), 1e-4)
mu0, var0 = models[0].predict_y(self.Xtest)
for i, m in enumerate(models[1:]):
mu, var = m.predict_y(self.Xtest)
assert_allclose(mu, mu0, 1e-3)
assert_allclose(var, var0, 1e-4)

class VGPTest(GPflowTestCase):
def test_vgp_vs_svgp(self):
with self.test_context():
N, Ns, DX, DY = 100, 10, 2, 2
np.random.seed(1)
X = np.random.randn(N, DX)
Xs = np.random.randn(Ns, DX)
Y = np.random.randn(N, DY)

kernel = gpflow.kernels.Matern52(DX)
likelihood = gpflow.likelihoods.StudentT()

m_svgp = gpflow.models.SVGP(
X, Y, kernel, likelihood, X.copy(), whiten=True, q_diag=False)
m_vgp = gpflow.models.VGP(X, Y, kernel, likelihood)

m_svgp.compile()
m_vgp.compile()

q_mu = np.random.randn(N, DY)
q_sqrt = np.random.randn(DY, N, N)

m_svgp.q_mu = q_mu
m_svgp.q_sqrt = q_sqrt

m_vgp.q_mu = q_mu
m_vgp.q_sqrt = q_sqrt

L_svgp = m_svgp.compute_log_likelihood()
L_vgp = m_vgp.compute_log_likelihood()
assert_allclose(L_svgp, L_vgp, rtol=1e-2)

pred_svgp = m_svgp.predict_f(Xs)
pred_vgp = m_vgp.predict_f(Xs)
assert_allclose(pred_svgp[0], pred_vgp[0])
assert_allclose(pred_svgp[1], pred_vgp[1])

def test_vgp_vs_opper_archambeau(self):
with self.test_context():
N, Ns, DX, DY = 100, 10, 2, 2

np.random.seed(1)
X = np.random.randn(N, DX)
Xs = np.random.randn(Ns, DX)
Y = np.random.randn(N, DY)

kernel = gpflow.kernels.Matern52(DX)
likelihood = gpflow.likelihoods.StudentT()

m_vgp = gpflow.models.VGP(X, Y, kernel, likelihood)
m_vgp_oa = gpflow.models.VGPOpperArchambeau(X, Y, kernel, likelihood)
m_vgp.compile()
m_vgp_oa.compile()

q_alpha = np.random.randn(N, DX)
q_lambda = np.random.randn(N, DX) ** 2

m_vgp_oa.q_alpha = q_alpha
m_vgp_oa.q_lambda = q_lambda

K = kernel.compute_K_symm(X) + np.eye(N) * default_jitter()
L = np.linalg.cholesky(K)
L_inv = np.linalg.inv(L)
K_inv = np.linalg.inv(K)

mean = K.dot(q_alpha)
prec_dnn = K_inv[None, :, :] + np.array([np.diag(l ** 2) for l in q_lambda.T])
var_dnn = np.linalg.inv(prec_dnn)

m_svgp_unwhitened = gpflow.models.SVGP(
X, Y, kernel, likelihood, X.copy(),
whiten=False, q_diag=False)

m_svgp_unwhitened.q_mu = mean
m_svgp_unwhitened.q_sqrt = np.linalg.cholesky(var_dnn)

m_svgp_unwhitened.compile()

mean_white_nd = L_inv.dot(mean)
var_white_dnn = np.einsum('nN,dNM,mM->dnm', L_inv, var_dnn, L_inv)

q_sqrt_nnd = np.linalg.cholesky(var_white_dnn)

m_vgp.q_mu = mean_white_nd
m_vgp.q_sqrt = q_sqrt_nnd

L_vgp = m_vgp.compute_log_likelihood()
L_svgp_unwhitened = m_svgp_unwhitened.compute_log_likelihood()
L_vgp_oa = m_vgp_oa.compute_log_likelihood()
assert_allclose(L_vgp, L_vgp_oa, rtol=1e-2)
assert_allclose(L_vgp, L_svgp_unwhitened, rtol=1e-2)

pred_vgp = m_vgp.predict_f(Xs)
pred_svgp_unwhitened = m_svgp_unwhitened.predict_f(Xs)
pred_vgp_oa = m_vgp_oa.predict_f(Xs)

assert_allclose(pred_vgp[0], pred_vgp_oa[0])
assert_allclose(pred_vgp[0], pred_svgp_unwhitened[0])
assert_allclose(pred_vgp[1], pred_vgp_oa[1], rtol=1e-4)  # jitter?
assert_allclose(pred_vgp[1], pred_svgp_unwhitened[1], rtol=1e-4)

#def test_recompile(self):
#    with self.test_context():
#        N, DX, DY = 100, 2, 2
#        np.random.seed(1)
#        X = np.random.randn(N, DX)
#        Y = np.random.randn(N, DY)
#        kernel = gpflow.kernels.Matern52(DX)
#        likelihood = gpflow.likelihoods.StudentT()
#        m_vgp = gpflow.models.VGP(X, Y, kernel, likelihood)
#        m_vgp_oa = gpflow.models.VGPOpperArchambeau(X, Y, kernel, likelihood)
#        for m in [m_vgp, m_vgp_oa]:
#            m.compile()
#            opt = gpflow.train.ScipyOptimizer()
#            opt.minimize(m, maxiter=1)
#            m.X = X[:-1, :]
#            m.Y = Y[:-1, :]
#            opt.minimize(m, maxiter=1)

class TestUpperBound(GPflowTestCase):
"""
Test for upper bound for regression marginal likelihood
"""

def setUp(self):
self.X = np.random.rand(100, 1)
self.Y = np.sin(1.5 * 2 * np.pi * self.X) + np.random.randn(*self.X.shape) * 0.1

def test_few_inducing_points(self):
with self.test_context() as session:
vfe = gpflow.models.SGPR(self.X, self.Y, gpflow.kernels.SquaredExponential(1), self.X[:10, :].copy())
opt = gpflow.train.ScipyOptimizer()
opt.minimize(vfe)

full = gpflow.models.GPR(self.X, self.Y, gpflow.kernels.SquaredExponential(1))