1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
|
"""
Testing for Gaussian Process module (sklearn.gaussian_process)
"""
# Author: Vincent Dubourg <vincent.dubourg@gmail.com>
# License: BSD style
from nose.tools import raises
from nose.tools import assert_true
import numpy as np
from sklearn.gaussian_process import GaussianProcess
from sklearn.gaussian_process import regression_models as regression
from sklearn.gaussian_process import correlation_models as correlation
def test_1d(regr=regression.constant, corr=correlation.squared_exponential,
random_start=10, beta0=None):
"""
MLE estimation of a one-dimensional Gaussian Process model.
Check random start optimization.
Test the interpolating property.
"""
f = lambda x: x * np.sin(x)
X = np.atleast_2d([1., 3., 5., 6., 7., 8.]).T
y = f(X).ravel()
gp = GaussianProcess(regr=regr, corr=corr, beta0=beta0,
theta0=1e-2, thetaL=1e-4, thetaU=1e-1,
random_start=random_start, verbose=False).fit(X, y)
y_pred, MSE = gp.predict(X, eval_MSE=True)
assert_true(np.allclose(y_pred, y) and np.allclose(MSE, 0.))
def test_2d(regr=regression.constant, corr=correlation.squared_exponential,
random_start=10, beta0=None):
"""
MLE estimation of a two-dimensional Gaussian Process model accounting for
anisotropy. Check random start optimization.
Test the interpolating property.
"""
b, kappa, e = 5., .5, .1
g = lambda x: b - x[:, 1] - kappa * (x[:, 0] - e) ** 2.
X = np.array([[-4.61611719, -6.00099547],
[4.10469096, 5.32782448],
[0.00000000, -0.50000000],
[-6.17289014, -4.6984743],
[1.3109306, -6.93271427],
[-5.03823144, 3.10584743],
[-2.87600388, 6.74310541],
[5.21301203, 4.26386883]])
y = g(X).ravel()
gp = GaussianProcess(regr=regr, corr=corr, beta0=beta0,
theta0=[1e-2] * 2, thetaL=[1e-4] * 2,
thetaU=[1e-1] * 2,
random_start=random_start, verbose=False)
gp.fit(X, y)
y_pred, MSE = gp.predict(X, eval_MSE=True)
assert_true(np.allclose(y_pred, y) and np.allclose(MSE, 0.))
@raises(ValueError)
def test_wrong_number_of_outputs():
gp = GaussianProcess()
gp.fit([[1, 2, 3], [4, 5, 6]], [1, 2, 3])
def test_more_builtin_correlation_models(random_start=1):
"""
Repeat test_1d and test_2d for several built-in correlation
models specified as strings.
"""
all_corr = ['absolute_exponential', 'squared_exponential', 'cubic',
'linear']
for corr in all_corr:
test_1d(regr='constant', corr=corr, random_start=random_start)
test_2d(regr='constant', corr=corr, random_start=random_start)
def test_ordinary_kriging():
"""
Repeat test_1d and test_2d with given regression weights (beta0) for
different regression models (Ordinary Kriging).
"""
test_1d(regr='linear', beta0=[0., 0.5])
test_1d(regr='quadratic', beta0=[0., 0.5, 0.5])
test_2d(regr='linear', beta0=[0., 0.5, 0.5])
test_2d(regr='quadratic', beta0=[0., 0.5, 0.5, 0.5, 0.5, 0.5])
|
