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"""Testing for Gaussian process classification """
# Author: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
# License: BSD 3 clause
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
from sklearn.utils.testing import (assert_true, assert_greater,
assert_almost_equal, assert_array_equal)
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)
@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_greater(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', 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_true(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_greater(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 50 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(50):
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_greater(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)
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