391 lines
13 KiB
Python
391 lines
13 KiB
Python
"""Testing for kernels for Gaussian processes."""
|
|
|
|
# Author: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
|
|
# License: BSD 3 clause
|
|
|
|
import pytest
|
|
import numpy as np
|
|
from inspect import signature
|
|
|
|
from sklearn.gaussian_process.kernels import _approx_fprime
|
|
|
|
from sklearn.metrics.pairwise import (
|
|
PAIRWISE_KERNEL_FUNCTIONS,
|
|
euclidean_distances,
|
|
pairwise_kernels,
|
|
)
|
|
from sklearn.gaussian_process.kernels import (
|
|
RBF,
|
|
Matern,
|
|
RationalQuadratic,
|
|
ExpSineSquared,
|
|
DotProduct,
|
|
ConstantKernel,
|
|
WhiteKernel,
|
|
PairwiseKernel,
|
|
KernelOperator,
|
|
Exponentiation,
|
|
CompoundKernel,
|
|
)
|
|
from sklearn.base import clone
|
|
|
|
from sklearn.utils._testing import (
|
|
assert_almost_equal,
|
|
assert_array_equal,
|
|
assert_array_almost_equal,
|
|
assert_allclose,
|
|
)
|
|
|
|
|
|
X = np.random.RandomState(0).normal(0, 1, (5, 2))
|
|
Y = np.random.RandomState(0).normal(0, 1, (6, 2))
|
|
|
|
kernel_rbf_plus_white = RBF(length_scale=2.0) + WhiteKernel(noise_level=3.0)
|
|
kernels = [
|
|
RBF(length_scale=2.0),
|
|
RBF(length_scale_bounds=(0.5, 2.0)),
|
|
ConstantKernel(constant_value=10.0),
|
|
2.0 * RBF(length_scale=0.33, length_scale_bounds="fixed"),
|
|
2.0 * RBF(length_scale=0.5),
|
|
kernel_rbf_plus_white,
|
|
2.0 * RBF(length_scale=[0.5, 2.0]),
|
|
2.0 * Matern(length_scale=0.33, length_scale_bounds="fixed"),
|
|
2.0 * Matern(length_scale=0.5, nu=0.5),
|
|
2.0 * Matern(length_scale=1.5, nu=1.5),
|
|
2.0 * Matern(length_scale=2.5, nu=2.5),
|
|
2.0 * Matern(length_scale=[0.5, 2.0], nu=0.5),
|
|
3.0 * Matern(length_scale=[2.0, 0.5], nu=1.5),
|
|
4.0 * Matern(length_scale=[0.5, 0.5], nu=2.5),
|
|
RationalQuadratic(length_scale=0.5, alpha=1.5),
|
|
ExpSineSquared(length_scale=0.5, periodicity=1.5),
|
|
DotProduct(sigma_0=2.0),
|
|
DotProduct(sigma_0=2.0) ** 2,
|
|
RBF(length_scale=[2.0]),
|
|
Matern(length_scale=[2.0]),
|
|
]
|
|
for metric in PAIRWISE_KERNEL_FUNCTIONS:
|
|
if metric in ["additive_chi2", "chi2"]:
|
|
continue
|
|
kernels.append(PairwiseKernel(gamma=1.0, metric=metric))
|
|
|
|
|
|
@pytest.mark.parametrize("kernel", kernels)
|
|
def test_kernel_gradient(kernel):
|
|
# Compare analytic and numeric gradient of kernels.
|
|
K, K_gradient = kernel(X, eval_gradient=True)
|
|
|
|
assert K_gradient.shape[0] == X.shape[0]
|
|
assert K_gradient.shape[1] == X.shape[0]
|
|
assert K_gradient.shape[2] == kernel.theta.shape[0]
|
|
|
|
def eval_kernel_for_theta(theta):
|
|
kernel_clone = kernel.clone_with_theta(theta)
|
|
K = kernel_clone(X, eval_gradient=False)
|
|
return K
|
|
|
|
K_gradient_approx = _approx_fprime(kernel.theta, eval_kernel_for_theta, 1e-10)
|
|
|
|
assert_almost_equal(K_gradient, K_gradient_approx, 4)
|
|
|
|
|
|
@pytest.mark.parametrize(
|
|
"kernel",
|
|
[
|
|
kernel
|
|
for kernel in kernels
|
|
# skip non-basic kernels
|
|
if not (isinstance(kernel, (KernelOperator, Exponentiation)))
|
|
],
|
|
)
|
|
def test_kernel_theta(kernel):
|
|
# Check that parameter vector theta of kernel is set correctly.
|
|
theta = kernel.theta
|
|
_, K_gradient = kernel(X, eval_gradient=True)
|
|
|
|
# Determine kernel parameters that contribute to theta
|
|
init_sign = signature(kernel.__class__.__init__).parameters.values()
|
|
args = [p.name for p in init_sign if p.name != "self"]
|
|
theta_vars = map(
|
|
lambda s: s[0 : -len("_bounds")], filter(lambda s: s.endswith("_bounds"), args)
|
|
)
|
|
assert set(hyperparameter.name for hyperparameter in kernel.hyperparameters) == set(
|
|
theta_vars
|
|
)
|
|
|
|
# Check that values returned in theta are consistent with
|
|
# hyperparameter values (being their logarithms)
|
|
for i, hyperparameter in enumerate(kernel.hyperparameters):
|
|
assert theta[i] == np.log(getattr(kernel, hyperparameter.name))
|
|
|
|
# Fixed kernel parameters must be excluded from theta and gradient.
|
|
for i, hyperparameter in enumerate(kernel.hyperparameters):
|
|
# create copy with certain hyperparameter fixed
|
|
params = kernel.get_params()
|
|
params[hyperparameter.name + "_bounds"] = "fixed"
|
|
kernel_class = kernel.__class__
|
|
new_kernel = kernel_class(**params)
|
|
# Check that theta and K_gradient are identical with the fixed
|
|
# dimension left out
|
|
_, K_gradient_new = new_kernel(X, eval_gradient=True)
|
|
assert theta.shape[0] == new_kernel.theta.shape[0] + 1
|
|
assert K_gradient.shape[2] == K_gradient_new.shape[2] + 1
|
|
if i > 0:
|
|
assert theta[:i] == new_kernel.theta[:i]
|
|
assert_array_equal(K_gradient[..., :i], K_gradient_new[..., :i])
|
|
if i + 1 < len(kernel.hyperparameters):
|
|
assert theta[i + 1 :] == new_kernel.theta[i:]
|
|
assert_array_equal(K_gradient[..., i + 1 :], K_gradient_new[..., i:])
|
|
|
|
# Check that values of theta are modified correctly
|
|
for i, hyperparameter in enumerate(kernel.hyperparameters):
|
|
theta[i] = np.log(42)
|
|
kernel.theta = theta
|
|
assert_almost_equal(getattr(kernel, hyperparameter.name), 42)
|
|
|
|
setattr(kernel, hyperparameter.name, 43)
|
|
assert_almost_equal(kernel.theta[i], np.log(43))
|
|
|
|
|
|
@pytest.mark.parametrize(
|
|
"kernel",
|
|
[
|
|
kernel
|
|
for kernel in kernels
|
|
# Identity is not satisfied on diagonal
|
|
if kernel != kernel_rbf_plus_white
|
|
],
|
|
)
|
|
def test_auto_vs_cross(kernel):
|
|
# Auto-correlation and cross-correlation should be consistent.
|
|
K_auto = kernel(X)
|
|
K_cross = kernel(X, X)
|
|
assert_almost_equal(K_auto, K_cross, 5)
|
|
|
|
|
|
@pytest.mark.parametrize("kernel", kernels)
|
|
def test_kernel_diag(kernel):
|
|
# Test that diag method of kernel returns consistent results.
|
|
K_call_diag = np.diag(kernel(X))
|
|
K_diag = kernel.diag(X)
|
|
assert_almost_equal(K_call_diag, K_diag, 5)
|
|
|
|
|
|
def test_kernel_operator_commutative():
|
|
# Adding kernels and multiplying kernels should be commutative.
|
|
# Check addition
|
|
assert_almost_equal((RBF(2.0) + 1.0)(X), (1.0 + RBF(2.0))(X))
|
|
|
|
# Check multiplication
|
|
assert_almost_equal((3.0 * RBF(2.0))(X), (RBF(2.0) * 3.0)(X))
|
|
|
|
|
|
def test_kernel_anisotropic():
|
|
# Anisotropic kernel should be consistent with isotropic kernels.
|
|
kernel = 3.0 * RBF([0.5, 2.0])
|
|
|
|
K = kernel(X)
|
|
X1 = np.array(X)
|
|
X1[:, 0] *= 4
|
|
K1 = 3.0 * RBF(2.0)(X1)
|
|
assert_almost_equal(K, K1)
|
|
|
|
X2 = np.array(X)
|
|
X2[:, 1] /= 4
|
|
K2 = 3.0 * RBF(0.5)(X2)
|
|
assert_almost_equal(K, K2)
|
|
|
|
# Check getting and setting via theta
|
|
kernel.theta = kernel.theta + np.log(2)
|
|
assert_array_equal(kernel.theta, np.log([6.0, 1.0, 4.0]))
|
|
assert_array_equal(kernel.k2.length_scale, [1.0, 4.0])
|
|
|
|
|
|
@pytest.mark.parametrize(
|
|
"kernel", [kernel for kernel in kernels if kernel.is_stationary()]
|
|
)
|
|
def test_kernel_stationary(kernel):
|
|
# Test stationarity of kernels.
|
|
K = kernel(X, X + 1)
|
|
assert_almost_equal(K[0, 0], np.diag(K))
|
|
|
|
|
|
@pytest.mark.parametrize("kernel", kernels)
|
|
def test_kernel_input_type(kernel):
|
|
# Test whether kernels is for vectors or structured data
|
|
if isinstance(kernel, Exponentiation):
|
|
assert kernel.requires_vector_input == kernel.kernel.requires_vector_input
|
|
if isinstance(kernel, KernelOperator):
|
|
assert kernel.requires_vector_input == (
|
|
kernel.k1.requires_vector_input or kernel.k2.requires_vector_input
|
|
)
|
|
|
|
|
|
def test_compound_kernel_input_type():
|
|
kernel = CompoundKernel([WhiteKernel(noise_level=3.0)])
|
|
assert not kernel.requires_vector_input
|
|
|
|
kernel = CompoundKernel([WhiteKernel(noise_level=3.0), RBF(length_scale=2.0)])
|
|
assert kernel.requires_vector_input
|
|
|
|
|
|
def check_hyperparameters_equal(kernel1, kernel2):
|
|
# Check that hyperparameters of two kernels are equal
|
|
for attr in set(dir(kernel1) + dir(kernel2)):
|
|
if attr.startswith("hyperparameter_"):
|
|
attr_value1 = getattr(kernel1, attr)
|
|
attr_value2 = getattr(kernel2, attr)
|
|
assert attr_value1 == attr_value2
|
|
|
|
|
|
@pytest.mark.parametrize("kernel", kernels)
|
|
def test_kernel_clone(kernel):
|
|
# Test that sklearn's clone works correctly on kernels.
|
|
kernel_cloned = clone(kernel)
|
|
|
|
# XXX: Should this be fixed?
|
|
# This differs from the sklearn's estimators equality check.
|
|
assert kernel == kernel_cloned
|
|
assert id(kernel) != id(kernel_cloned)
|
|
|
|
# Check that all constructor parameters are equal.
|
|
assert kernel.get_params() == kernel_cloned.get_params()
|
|
|
|
# Check that all hyperparameters are equal.
|
|
check_hyperparameters_equal(kernel, kernel_cloned)
|
|
|
|
|
|
@pytest.mark.parametrize("kernel", kernels)
|
|
def test_kernel_clone_after_set_params(kernel):
|
|
# This test is to verify that using set_params does not
|
|
# break clone on kernels.
|
|
# This used to break because in kernels such as the RBF, non-trivial
|
|
# logic that modified the length scale used to be in the constructor
|
|
# See https://github.com/scikit-learn/scikit-learn/issues/6961
|
|
# for more details.
|
|
bounds = (1e-5, 1e5)
|
|
kernel_cloned = clone(kernel)
|
|
params = kernel.get_params()
|
|
# RationalQuadratic kernel is isotropic.
|
|
isotropic_kernels = (ExpSineSquared, RationalQuadratic)
|
|
if "length_scale" in params and not isinstance(kernel, isotropic_kernels):
|
|
length_scale = params["length_scale"]
|
|
if np.iterable(length_scale):
|
|
# XXX unreached code as of v0.22
|
|
params["length_scale"] = length_scale[0]
|
|
params["length_scale_bounds"] = bounds
|
|
else:
|
|
params["length_scale"] = [length_scale] * 2
|
|
params["length_scale_bounds"] = bounds * 2
|
|
kernel_cloned.set_params(**params)
|
|
kernel_cloned_clone = clone(kernel_cloned)
|
|
assert kernel_cloned_clone.get_params() == kernel_cloned.get_params()
|
|
assert id(kernel_cloned_clone) != id(kernel_cloned)
|
|
check_hyperparameters_equal(kernel_cloned, kernel_cloned_clone)
|
|
|
|
|
|
def test_matern_kernel():
|
|
# Test consistency of Matern kernel for special values of nu.
|
|
K = Matern(nu=1.5, length_scale=1.0)(X)
|
|
# the diagonal elements of a matern kernel are 1
|
|
assert_array_almost_equal(np.diag(K), np.ones(X.shape[0]))
|
|
# matern kernel for coef0==0.5 is equal to absolute exponential kernel
|
|
K_absexp = np.exp(-euclidean_distances(X, X, squared=False))
|
|
K = Matern(nu=0.5, length_scale=1.0)(X)
|
|
assert_array_almost_equal(K, K_absexp)
|
|
# matern kernel with coef0==inf is equal to RBF kernel
|
|
K_rbf = RBF(length_scale=1.0)(X)
|
|
K = Matern(nu=np.inf, length_scale=1.0)(X)
|
|
assert_array_almost_equal(K, K_rbf)
|
|
assert_allclose(K, K_rbf)
|
|
# test that special cases of matern kernel (coef0 in [0.5, 1.5, 2.5])
|
|
# result in nearly identical results as the general case for coef0 in
|
|
# [0.5 + tiny, 1.5 + tiny, 2.5 + tiny]
|
|
tiny = 1e-10
|
|
for nu in [0.5, 1.5, 2.5]:
|
|
K1 = Matern(nu=nu, length_scale=1.0)(X)
|
|
K2 = Matern(nu=nu + tiny, length_scale=1.0)(X)
|
|
assert_array_almost_equal(K1, K2)
|
|
# test that coef0==large is close to RBF
|
|
large = 100
|
|
K1 = Matern(nu=large, length_scale=1.0)(X)
|
|
K2 = RBF(length_scale=1.0)(X)
|
|
assert_array_almost_equal(K1, K2, decimal=2)
|
|
|
|
|
|
@pytest.mark.parametrize("kernel", kernels)
|
|
def test_kernel_versus_pairwise(kernel):
|
|
# Check that GP kernels can also be used as pairwise kernels.
|
|
|
|
# Test auto-kernel
|
|
if kernel != kernel_rbf_plus_white:
|
|
# For WhiteKernel: k(X) != k(X,X). This is assumed by
|
|
# pairwise_kernels
|
|
K1 = kernel(X)
|
|
K2 = pairwise_kernels(X, metric=kernel)
|
|
assert_array_almost_equal(K1, K2)
|
|
|
|
# Test cross-kernel
|
|
K1 = kernel(X, Y)
|
|
K2 = pairwise_kernels(X, Y, metric=kernel)
|
|
assert_array_almost_equal(K1, K2)
|
|
|
|
|
|
@pytest.mark.parametrize("kernel", kernels)
|
|
def test_set_get_params(kernel):
|
|
# Check that set_params()/get_params() is consistent with kernel.theta.
|
|
|
|
# Test get_params()
|
|
index = 0
|
|
params = kernel.get_params()
|
|
for hyperparameter in kernel.hyperparameters:
|
|
if isinstance("string", type(hyperparameter.bounds)):
|
|
if hyperparameter.bounds == "fixed":
|
|
continue
|
|
size = hyperparameter.n_elements
|
|
if size > 1: # anisotropic kernels
|
|
assert_almost_equal(
|
|
np.exp(kernel.theta[index : index + size]), params[hyperparameter.name]
|
|
)
|
|
index += size
|
|
else:
|
|
assert_almost_equal(
|
|
np.exp(kernel.theta[index]), params[hyperparameter.name]
|
|
)
|
|
index += 1
|
|
# Test set_params()
|
|
index = 0
|
|
value = 10 # arbitrary value
|
|
for hyperparameter in kernel.hyperparameters:
|
|
if isinstance("string", type(hyperparameter.bounds)):
|
|
if hyperparameter.bounds == "fixed":
|
|
continue
|
|
size = hyperparameter.n_elements
|
|
if size > 1: # anisotropic kernels
|
|
kernel.set_params(**{hyperparameter.name: [value] * size})
|
|
assert_almost_equal(
|
|
np.exp(kernel.theta[index : index + size]), [value] * size
|
|
)
|
|
index += size
|
|
else:
|
|
kernel.set_params(**{hyperparameter.name: value})
|
|
assert_almost_equal(np.exp(kernel.theta[index]), value)
|
|
index += 1
|
|
|
|
|
|
@pytest.mark.parametrize("kernel", kernels)
|
|
def test_repr_kernels(kernel):
|
|
# Smoke-test for repr in kernels.
|
|
|
|
repr(kernel)
|
|
|
|
|
|
def test_rational_quadratic_kernel():
|
|
kernel = RationalQuadratic(length_scale=[1.0, 1.0])
|
|
message = (
|
|
"RationalQuadratic kernel only supports isotropic "
|
|
"version, please use a single "
|
|
"scalar for length_scale"
|
|
)
|
|
with pytest.raises(AttributeError, match=message):
|
|
kernel(X)
|