138 lines
4.7 KiB
Python
138 lines
4.7 KiB
Python
"""
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Testing for Gaussian Process module (sklearn.gaussian_process)
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"""
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# Author: Vincent Dubourg <vincent.dubourg@gmail.com>
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# Licence: BSD 3 clause
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from nose.tools import raises
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from nose.tools import assert_true
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import numpy as np
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from sklearn.gaussian_process import GaussianProcess
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from sklearn.gaussian_process import regression_models as regression
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from sklearn.gaussian_process import correlation_models as correlation
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f = lambda x: x * np.sin(x)
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X = np.atleast_2d([1., 3., 5., 6., 7., 8.]).T
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X2 = np.atleast_2d([2., 4., 5.5, 6.5, 7.5]).T
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y = f(X).ravel()
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def test_1d(regr=regression.constant, corr=correlation.squared_exponential,
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random_start=10, beta0=None):
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"""
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MLE estimation of a one-dimensional Gaussian Process model.
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Check random start optimization.
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Test the interpolating property.
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"""
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gp = GaussianProcess(regr=regr, corr=corr, beta0=beta0,
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theta0=1e-2, thetaL=1e-4, thetaU=1e-1,
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random_start=random_start, verbose=False).fit(X, y)
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y_pred, MSE = gp.predict(X, eval_MSE=True)
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y2_pred, MSE2 = gp.predict(X2, eval_MSE=True)
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assert_true(np.allclose(y_pred, y) and np.allclose(MSE, 0.)
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and np.allclose(MSE2, 0., atol=10))
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def test_2d(regr=regression.constant, corr=correlation.squared_exponential,
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random_start=10, beta0=None):
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"""
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MLE estimation of a two-dimensional Gaussian Process model accounting for
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anisotropy. Check random start optimization.
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Test the interpolating property.
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"""
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b, kappa, e = 5., .5, .1
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g = lambda x: b - x[:, 1] - kappa * (x[:, 0] - e) ** 2.
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X = np.array([[-4.61611719, -6.00099547],
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[4.10469096, 5.32782448],
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[0.00000000, -0.50000000],
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[-6.17289014, -4.6984743],
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[1.3109306, -6.93271427],
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[-5.03823144, 3.10584743],
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[-2.87600388, 6.74310541],
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[5.21301203, 4.26386883]])
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y = g(X).ravel()
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gp = GaussianProcess(regr=regr, corr=corr, beta0=beta0,
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theta0=[1e-2] * 2, thetaL=[1e-4] * 2,
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thetaU=[1e-1] * 2,
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random_start=random_start, verbose=False)
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gp.fit(X, y)
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y_pred, MSE = gp.predict(X, eval_MSE=True)
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assert_true(np.allclose(y_pred, y) and np.allclose(MSE, 0.))
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def test_2d_2d(regr=regression.constant, corr=correlation.squared_exponential,
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random_start=10, beta0=None):
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"""
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MLE estimation of a two-dimensional Gaussian Process model accounting for
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anisotropy. Check random start optimization.
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Test the GP interpolation for 2D output
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"""
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b, kappa, e = 5., .5, .1
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g = lambda x: b - x[:, 1] - kappa * (x[:, 0] - e) ** 2.
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f = lambda x: np.vstack((g(x), g(x))).T
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X = np.array([[-4.61611719, -6.00099547],
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[4.10469096, 5.32782448],
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[0.00000000, -0.50000000],
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[-6.17289014, -4.6984743],
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[1.3109306, -6.93271427],
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[-5.03823144, 3.10584743],
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[-2.87600388, 6.74310541],
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[5.21301203, 4.26386883]])
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y = f(X)
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gp = GaussianProcess(regr=regr, corr=corr, beta0=beta0,
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theta0=[1e-2] * 2, thetaL=[1e-4] * 2,
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thetaU=[1e-1] * 2,
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random_start=random_start, verbose=False)
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gp.fit(X, y)
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y_pred, MSE = gp.predict(X, eval_MSE=True)
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assert_true(np.allclose(y_pred, y) and np.allclose(MSE, 0.))
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@raises(ValueError)
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def test_wrong_number_of_outputs():
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gp = GaussianProcess()
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gp.fit([[1, 2, 3], [4, 5, 6]], [1, 2, 3])
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def test_more_builtin_correlation_models(random_start=1):
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"""
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Repeat test_1d and test_2d for several built-in correlation
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models specified as strings.
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"""
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all_corr = ['absolute_exponential', 'squared_exponential', 'cubic',
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'linear']
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for corr in all_corr:
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test_1d(regr='constant', corr=corr, random_start=random_start)
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test_2d(regr='constant', corr=corr, random_start=random_start)
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test_2d_2d(regr='constant', corr=corr, random_start=random_start)
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def test_ordinary_kriging():
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"""
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Repeat test_1d and test_2d with given regression weights (beta0) for
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different regression models (Ordinary Kriging).
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"""
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test_1d(regr='linear', beta0=[0., 0.5])
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test_1d(regr='quadratic', beta0=[0., 0.5, 0.5])
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test_2d(regr='linear', beta0=[0., 0.5, 0.5])
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test_2d(regr='quadratic', beta0=[0., 0.5, 0.5, 0.5, 0.5, 0.5])
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test_2d_2d(regr='linear', beta0=[0., 0.5, 0.5])
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test_2d_2d(regr='quadratic', beta0=[0., 0.5, 0.5, 0.5, 0.5, 0.5])
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def test_no_normalize():
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gp = GaussianProcess(normalize=False).fit(X, y)
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y_pred = gp.predict(X)
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assert_true(np.allclose(y_pred, y))
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