250 lines
10 KiB
Python
250 lines
10 KiB
Python
"""Testing for Gaussian process classification """
|
|
|
|
# Author: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
|
|
# License: BSD 3 clause
|
|
|
|
import warnings
|
|
import numpy as np
|
|
|
|
from scipy.optimize import approx_fprime
|
|
|
|
import pytest
|
|
|
|
from sklearn.gaussian_process import GaussianProcessClassifier
|
|
from sklearn.gaussian_process.kernels \
|
|
import RBF, ConstantKernel as C, WhiteKernel
|
|
from sklearn.gaussian_process.tests._mini_sequence_kernel import MiniSeqKernel
|
|
from sklearn.exceptions import ConvergenceWarning
|
|
|
|
from sklearn.utils._testing \
|
|
import assert_almost_equal, assert_array_equal, assert_warns_message
|
|
|
|
|
|
def f(x):
|
|
return np.sin(x)
|
|
|
|
|
|
X = np.atleast_2d(np.linspace(0, 10, 30)).T
|
|
X2 = np.atleast_2d([2., 4., 5.5, 6.5, 7.5]).T
|
|
y = np.array(f(X).ravel() > 0, dtype=int)
|
|
fX = f(X).ravel()
|
|
y_mc = np.empty(y.shape, dtype=int) # multi-class
|
|
y_mc[fX < -0.35] = 0
|
|
y_mc[(fX >= -0.35) & (fX < 0.35)] = 1
|
|
y_mc[fX > 0.35] = 2
|
|
|
|
|
|
fixed_kernel = RBF(length_scale=1.0, length_scale_bounds="fixed")
|
|
kernels = [RBF(length_scale=0.1), fixed_kernel,
|
|
RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3)),
|
|
C(1.0, (1e-2, 1e2)) *
|
|
RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3))]
|
|
non_fixed_kernels = [kernel for kernel in kernels
|
|
if kernel != fixed_kernel]
|
|
|
|
|
|
@pytest.mark.parametrize('kernel', kernels)
|
|
def test_predict_consistent(kernel):
|
|
# Check binary predict decision has also predicted probability above 0.5.
|
|
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
|
|
assert_array_equal(gpc.predict(X),
|
|
gpc.predict_proba(X)[:, 1] >= 0.5)
|
|
|
|
|
|
def test_predict_consistent_structured():
|
|
# Check binary predict decision has also predicted probability above 0.5.
|
|
X = ['A', 'AB', 'B']
|
|
y = np.array([True, False, True])
|
|
kernel = MiniSeqKernel(baseline_similarity_bounds='fixed')
|
|
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
|
|
assert_array_equal(gpc.predict(X),
|
|
gpc.predict_proba(X)[:, 1] >= 0.5)
|
|
|
|
|
|
@pytest.mark.parametrize('kernel', non_fixed_kernels)
|
|
def test_lml_improving(kernel):
|
|
# Test that hyperparameter-tuning improves log-marginal likelihood.
|
|
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
|
|
assert (gpc.log_marginal_likelihood(gpc.kernel_.theta) >
|
|
gpc.log_marginal_likelihood(kernel.theta))
|
|
|
|
|
|
@pytest.mark.parametrize('kernel', kernels)
|
|
def test_lml_precomputed(kernel):
|
|
# Test that lml of optimized kernel is stored correctly.
|
|
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
|
|
assert_almost_equal(gpc.log_marginal_likelihood(gpc.kernel_.theta),
|
|
gpc.log_marginal_likelihood(), 7)
|
|
|
|
|
|
@pytest.mark.parametrize('kernel', kernels)
|
|
def test_lml_without_cloning_kernel(kernel):
|
|
# Test that clone_kernel=False has side-effects of kernel.theta.
|
|
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
|
|
input_theta = np.ones(gpc.kernel_.theta.shape, dtype=np.float64)
|
|
|
|
gpc.log_marginal_likelihood(input_theta, clone_kernel=False)
|
|
assert_almost_equal(gpc.kernel_.theta, input_theta, 7)
|
|
|
|
|
|
@pytest.mark.parametrize('kernel', non_fixed_kernels)
|
|
def test_converged_to_local_maximum(kernel):
|
|
# Test that we are in local maximum after hyperparameter-optimization.
|
|
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
|
|
|
|
lml, lml_gradient = \
|
|
gpc.log_marginal_likelihood(gpc.kernel_.theta, True)
|
|
|
|
assert np.all((np.abs(lml_gradient) < 1e-4) |
|
|
(gpc.kernel_.theta == gpc.kernel_.bounds[:, 0]) |
|
|
(gpc.kernel_.theta == gpc.kernel_.bounds[:, 1]))
|
|
|
|
|
|
@pytest.mark.parametrize('kernel', kernels)
|
|
def test_lml_gradient(kernel):
|
|
# Compare analytic and numeric gradient of log marginal likelihood.
|
|
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
|
|
|
|
lml, lml_gradient = gpc.log_marginal_likelihood(kernel.theta, True)
|
|
lml_gradient_approx = \
|
|
approx_fprime(kernel.theta,
|
|
lambda theta: gpc.log_marginal_likelihood(theta,
|
|
False),
|
|
1e-10)
|
|
|
|
assert_almost_equal(lml_gradient, lml_gradient_approx, 3)
|
|
|
|
|
|
def test_random_starts():
|
|
# Test that an increasing number of random-starts of GP fitting only
|
|
# increases the log marginal likelihood of the chosen theta.
|
|
n_samples, n_features = 25, 2
|
|
rng = np.random.RandomState(0)
|
|
X = rng.randn(n_samples, n_features) * 2 - 1
|
|
y = (np.sin(X).sum(axis=1) + np.sin(3 * X).sum(axis=1)) > 0
|
|
|
|
kernel = C(1.0, (1e-2, 1e2)) \
|
|
* RBF(length_scale=[1e-3] * n_features,
|
|
length_scale_bounds=[(1e-4, 1e+2)] * n_features)
|
|
last_lml = -np.inf
|
|
for n_restarts_optimizer in range(5):
|
|
gp = GaussianProcessClassifier(
|
|
kernel=kernel, n_restarts_optimizer=n_restarts_optimizer,
|
|
random_state=0).fit(X, y)
|
|
lml = gp.log_marginal_likelihood(gp.kernel_.theta)
|
|
assert lml > last_lml - np.finfo(np.float32).eps
|
|
last_lml = lml
|
|
|
|
|
|
@pytest.mark.parametrize('kernel', non_fixed_kernels)
|
|
def test_custom_optimizer(kernel):
|
|
# Test that GPC can use externally defined optimizers.
|
|
# Define a dummy optimizer that simply tests 10 random hyperparameters
|
|
def optimizer(obj_func, initial_theta, bounds):
|
|
rng = np.random.RandomState(0)
|
|
theta_opt, func_min = \
|
|
initial_theta, obj_func(initial_theta, eval_gradient=False)
|
|
for _ in range(10):
|
|
theta = np.atleast_1d(rng.uniform(np.maximum(-2, bounds[:, 0]),
|
|
np.minimum(1, bounds[:, 1])))
|
|
f = obj_func(theta, eval_gradient=False)
|
|
if f < func_min:
|
|
theta_opt, func_min = theta, f
|
|
return theta_opt, func_min
|
|
|
|
gpc = GaussianProcessClassifier(kernel=kernel, optimizer=optimizer)
|
|
gpc.fit(X, y_mc)
|
|
# Checks that optimizer improved marginal likelihood
|
|
assert (gpc.log_marginal_likelihood(gpc.kernel_.theta) >
|
|
gpc.log_marginal_likelihood(kernel.theta))
|
|
|
|
|
|
@pytest.mark.parametrize('kernel', kernels)
|
|
def test_multi_class(kernel):
|
|
# Test GPC for multi-class classification problems.
|
|
gpc = GaussianProcessClassifier(kernel=kernel)
|
|
gpc.fit(X, y_mc)
|
|
|
|
y_prob = gpc.predict_proba(X2)
|
|
assert_almost_equal(y_prob.sum(1), 1)
|
|
|
|
y_pred = gpc.predict(X2)
|
|
assert_array_equal(np.argmax(y_prob, 1), y_pred)
|
|
|
|
|
|
@pytest.mark.parametrize('kernel', kernels)
|
|
def test_multi_class_n_jobs(kernel):
|
|
# Test that multi-class GPC produces identical results with n_jobs>1.
|
|
gpc = GaussianProcessClassifier(kernel=kernel)
|
|
gpc.fit(X, y_mc)
|
|
|
|
gpc_2 = GaussianProcessClassifier(kernel=kernel, n_jobs=2)
|
|
gpc_2.fit(X, y_mc)
|
|
|
|
y_prob = gpc.predict_proba(X2)
|
|
y_prob_2 = gpc_2.predict_proba(X2)
|
|
assert_almost_equal(y_prob, y_prob_2)
|
|
|
|
|
|
def test_warning_bounds():
|
|
kernel = RBF(length_scale_bounds=[1e-5, 1e-3])
|
|
gpc = GaussianProcessClassifier(kernel=kernel)
|
|
assert_warns_message(ConvergenceWarning, "The optimal value found for "
|
|
"dimension 0 of parameter "
|
|
"length_scale is close to "
|
|
"the specified upper bound "
|
|
"0.001. Increasing the bound "
|
|
"and calling fit again may "
|
|
"find a better value.",
|
|
gpc.fit, X, y)
|
|
|
|
kernel_sum = (WhiteKernel(noise_level_bounds=[1e-5, 1e-3]) +
|
|
RBF(length_scale_bounds=[1e3, 1e5]))
|
|
gpc_sum = GaussianProcessClassifier(kernel=kernel_sum)
|
|
with pytest.warns(None) as record:
|
|
with warnings.catch_warnings():
|
|
# scipy 1.3.0 uses tostring which is deprecated in numpy
|
|
warnings.filterwarnings("ignore", "tostring", DeprecationWarning)
|
|
gpc_sum.fit(X, y)
|
|
|
|
assert len(record) == 2
|
|
assert record[0].message.args[0] == ("The optimal value found for "
|
|
"dimension 0 of parameter "
|
|
"k1__noise_level is close to the "
|
|
"specified upper bound 0.001. "
|
|
"Increasing the bound and calling "
|
|
"fit again may find a better value.")
|
|
|
|
assert record[1].message.args[0] == ("The optimal value found for "
|
|
"dimension 0 of parameter "
|
|
"k2__length_scale is close to the "
|
|
"specified lower bound 1000.0. "
|
|
"Decreasing the bound and calling "
|
|
"fit again may find a better value.")
|
|
|
|
X_tile = np.tile(X, 2)
|
|
kernel_dims = RBF(length_scale=[1., 2.],
|
|
length_scale_bounds=[1e1, 1e2])
|
|
gpc_dims = GaussianProcessClassifier(kernel=kernel_dims)
|
|
|
|
with pytest.warns(None) as record:
|
|
with warnings.catch_warnings():
|
|
# scipy 1.3.0 uses tostring which is deprecated in numpy
|
|
warnings.filterwarnings("ignore", "tostring", DeprecationWarning)
|
|
gpc_dims.fit(X_tile, y)
|
|
|
|
assert len(record) == 2
|
|
assert record[0].message.args[0] == ("The optimal value found for "
|
|
"dimension 0 of parameter "
|
|
"length_scale is close to the "
|
|
"specified upper bound 100.0. "
|
|
"Increasing the bound and calling "
|
|
"fit again may find a better value.")
|
|
|
|
assert record[1].message.args[0] == ("The optimal value found for "
|
|
"dimension 1 of parameter "
|
|
"length_scale is close to the "
|
|
"specified upper bound 100.0. "
|
|
"Increasing the bound and calling "
|
|
"fit again may find a better value.")
|