test_priors.py
# Copyright 2016 the gpflow authors.
#
# 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 tensorflow as tf
import numpy as np
from numpy.testing import assert_allclose
import pytest
import gpflow
from gpflow import settings
from gpflow.test_util import GPflowTestCase
class FlatModel(gpflow.models.Model):
def _build_likelihood(self):
return np.array(0., dtype=settings.float_type)
class TestPriorMode(GPflowTestCase):
"""
these tests optimize the prior to find the mode numerically. Make sure the
mode is the same as the known mode.
"""
def prepare(self, autobuild=False):
return FlatModel(autobuild=autobuild)
def testGaussianMode(self):
with self.test_context():
m = self.prepare()
m.x = gpflow.Param(1., autobuild=False)
m.x.prior = gpflow.priors.Gaussian(3., 1.)
m.compile()
opt = gpflow.train.ScipyOptimizer()
opt.minimize(m)
_ = [assert_allclose(v, 3) for v in m.read_trainables().values()]
def testGaussianModeMatrix(self):
with self.test_context():
m = self.prepare()
m.x = gpflow.Param(np.random.randn(4, 4), prior=gpflow.priors.Gaussian(-1., 10.))
m.compile()
opt = gpflow.train.ScipyOptimizer()
opt.minimize(m)
_ = [assert_allclose(v, -1.) for v in m.read_trainables().values()]
def testExponential(self):
with self.test_context():
m = self.prepare()
m.x = gpflow.Param(1.0, prior=gpflow.priors.Exponential(1.0))
m.compile()
self.assertTrue(np.allclose(m.compute_log_prior(), -1.0))
with self.test_context():
m = self.prepare()
m.x = gpflow.Param(1.0, prior=gpflow.priors.Exponential(2.0))
m.compile()
self.assertTrue(np.allclose(m.compute_log_prior(), np.log(2) - 2))
def testGammaMode(self):
with self.test_context():
m = self.prepare()
m.x = gpflow.Param(1.0, autobuild=False)
shape, scale = 4., 5.
m.x.prior = gpflow.priors.Gamma(shape, scale)
m.compile()
opt = gpflow.train.ScipyOptimizer()
opt.minimize(m)
true_mode = (shape - 1.) * scale
assert_allclose(m.x.read_value(), true_mode, 1e-3)
def testLaplaceMode(self):
with self.test_context():
m = self.prepare()
m.x = gpflow.Param(1.0, prior=gpflow.priors.Laplace(3., 10.))
m.compile()
opt = gpflow.train.ScipyOptimizer()
opt.minimize(m)
_ = [assert_allclose(v, 3) for v in m.read_trainables().values()]
def testLogNormalMode(self):
with self.test_context():
m = self.prepare()
transform = gpflow.transforms.Exp()
prior = gpflow.priors.LogNormal(3., 10.)
m.x = gpflow.Param(1.0, prior=prior, transform=transform)
m.compile()
opt = gpflow.train.ScipyOptimizer()
opt.minimize(m)
xmax = [transform.backward(x) for x in m.read_trainables().values()]
assert_allclose(xmax, 3, rtol=1e4)
def testBetaMode(self):
with self.test_context():
m = self.prepare()
transform = gpflow.transforms.Logistic()
m.x = gpflow.Param(0.1, prior=gpflow.priors.Beta(3., 3.), transform=transform)
m.compile()
opt = gpflow.train.ScipyOptimizer()
opt.minimize(m)
xmax = [transform.backward(x) for x in m.read_trainables().values()]
assert_allclose(0.0, xmax, atol=1.e-5)
def testUniform(self):
with self.test_context():
m = self.prepare()
m.x = gpflow.Param(
1.0, prior=gpflow.priors.Uniform(-2., 3.),
transform=gpflow.transforms.Logistic(-2., 3.))
m.compile()
m.x = np.random.randn(1)[0]
p1 = m.compute_log_prior()
m.x = np.random.randn(1)[0]
p2 = m.compute_log_prior()
# prior should not be the same because a transformation has been applied.
self.assertTrue(p1 != p2)
def mc_moments(prior, size=(10000, 1000)):
np.random.seed(1)
x = prior.sample(size)
assert x.shape == size, "inline test that .sample() returns correct shape"
mean = x.mean()
var = x.var()
# analytic moments are all np.atleast_1d() due to the parameters in gpflow.priors
# hence we need to do the same for the MC moments so that the shapes match
return np.atleast_1d(mean), np.atleast_1d(var)
def gaussian_moments(prior):
return prior.mu, prior.var
def exponential_moments(prior):
return 1 / prior.rate, prior.rate ** (-2)
def lognormal_moments(prior):
mu, var = prior.mu, prior.var
return np.exp(mu + var / 2), (np.exp(var) - 1) * np.exp(2 * mu + var)
def gamma_moments(prior):
return prior.shape * prior.scale, prior.shape * prior.scale ** 2
def laplace_moments(prior):
return prior.mu, 2 * prior.sigma ** 2
def beta_moments(prior):
a, b = prior.a, prior.b
return a / (a + b), (a * b) / ((a + b)**2 * (a + b + 1))
def uniform_moments(prior):
a, b = prior.lower, prior.upper
# this is the only prior that does not wrap parameters in np.atleast_1d()
# so do it here to make sure all the shapes are consistent:
a = np.atleast_1d(a)
b = np.atleast_1d(b)
return (a + b) / 2, (b - a)**2 / 12
@pytest.mark.parametrize("args", [
("Exponential", [1.3]),
("Gaussian", [-2.5, 3.4]),
("LogNormal", [-2.5, 1.4]),
("Gamma", [1.5, 0.7]),
("Laplace", [-2.5, 3.4]),
("Beta", [3.6, 0.4]),
("Uniform", [5.4, 8.9]),
])
def test_moments(args):
classname, params = args
cls = eval("gpflow.priors.{}".format(classname))
prior = cls(*params)
moments_func = eval("{}_moments".format(cls.__name__.lower()))
rtol = 5e-3 if classname == "LogNormal" else 1e-3
assert_allclose(moments_func(prior), mc_moments(prior), rtol=rtol,
err_msg="for {} prior".format(classname))
if __name__ == "__main__":
tf.test.main()
