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
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
|
"""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
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))]
def test_predict_consistent():
# Check binary predict decision has also predicted probability above 0.5.
for kernel in kernels:
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
assert_array_equal(gpc.predict(X),
gpc.predict_proba(X)[:, 1] >= 0.5)
def test_lml_improving():
# Test that hyperparameter-tuning improves log-marginal likelihood.
for kernel in kernels:
if kernel == fixed_kernel:
continue
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
assert_greater(gpc.log_marginal_likelihood(gpc.kernel_.theta),
gpc.log_marginal_likelihood(kernel.theta))
def test_lml_precomputed():
# Test that lml of optimized kernel is stored correctly.
for kernel in kernels:
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
assert_almost_equal(gpc.log_marginal_likelihood(gpc.kernel_.theta),
gpc.log_marginal_likelihood(), 7)
def test_converged_to_local_maximum():
# Test that we are in local maximum after hyperparameter-optimization.
for kernel in kernels:
if kernel == fixed_kernel:
continue
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])))
def test_lml_gradient():
# Compare analytic and numeric gradient of log marginal likelihood.
for kernel in kernels:
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
np.random.seed(0)
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
def test_custom_optimizer():
# 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
for kernel in kernels:
if kernel == fixed_kernel:
continue
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))
def test_multi_class():
# Test GPC for multi-class classification problems.
for kernel in kernels:
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)
def test_multi_class_n_jobs():
# Test that multi-class GPC produces identical results with n_jobs>1.
for kernel in kernels:
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)
|
