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
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
|
import numpy as np
import pytest
from sklearn.utils.testing import (assert_allclose, assert_raises,
assert_equal)
from sklearn.neighbors import KernelDensity, KDTree, NearestNeighbors
from sklearn.neighbors.ball_tree import kernel_norm
from sklearn.pipeline import make_pipeline
from sklearn.datasets import make_blobs
from sklearn.model_selection import GridSearchCV
from sklearn.preprocessing import StandardScaler
from sklearn.utils import _joblib
def compute_kernel_slow(Y, X, kernel, h):
d = np.sqrt(((Y[:, None, :] - X) ** 2).sum(-1))
norm = kernel_norm(h, X.shape[1], kernel) / X.shape[0]
if kernel == 'gaussian':
return norm * np.exp(-0.5 * (d * d) / (h * h)).sum(-1)
elif kernel == 'tophat':
return norm * (d < h).sum(-1)
elif kernel == 'epanechnikov':
return norm * ((1.0 - (d * d) / (h * h)) * (d < h)).sum(-1)
elif kernel == 'exponential':
return norm * (np.exp(-d / h)).sum(-1)
elif kernel == 'linear':
return norm * ((1 - d / h) * (d < h)).sum(-1)
elif kernel == 'cosine':
return norm * (np.cos(0.5 * np.pi * d / h) * (d < h)).sum(-1)
else:
raise ValueError('kernel not recognized')
def check_results(kernel, bandwidth, atol, rtol, X, Y, dens_true):
kde = KernelDensity(kernel=kernel, bandwidth=bandwidth,
atol=atol, rtol=rtol)
log_dens = kde.fit(X).score_samples(Y)
assert_allclose(np.exp(log_dens), dens_true,
atol=atol, rtol=max(1E-7, rtol))
assert_allclose(np.exp(kde.score(Y)),
np.prod(dens_true),
atol=atol, rtol=max(1E-7, rtol))
@pytest.mark.parametrize(
'kernel',
['gaussian', 'tophat', 'epanechnikov',
'exponential', 'linear', 'cosine'])
@pytest.mark.parametrize('bandwidth', [0.01, 0.1, 1])
def test_kernel_density(kernel, bandwidth):
n_samples, n_features = (100, 3)
rng = np.random.RandomState(0)
X = rng.randn(n_samples, n_features)
Y = rng.randn(n_samples, n_features)
dens_true = compute_kernel_slow(Y, X, kernel, bandwidth)
for rtol in [0, 1E-5]:
for atol in [1E-6, 1E-2]:
for breadth_first in (True, False):
check_results(kernel, bandwidth, atol, rtol,
X, Y, dens_true)
def test_kernel_density_sampling(n_samples=100, n_features=3):
rng = np.random.RandomState(0)
X = rng.randn(n_samples, n_features)
bandwidth = 0.2
for kernel in ['gaussian', 'tophat']:
# draw a tophat sample
kde = KernelDensity(bandwidth, kernel=kernel).fit(X)
samp = kde.sample(100)
assert_equal(X.shape, samp.shape)
# check that samples are in the right range
nbrs = NearestNeighbors(n_neighbors=1).fit(X)
dist, ind = nbrs.kneighbors(X, return_distance=True)
if kernel == 'tophat':
assert np.all(dist < bandwidth)
elif kernel == 'gaussian':
# 5 standard deviations is safe for 100 samples, but there's a
# very small chance this test could fail.
assert np.all(dist < 5 * bandwidth)
# check unsupported kernels
for kernel in ['epanechnikov', 'exponential', 'linear', 'cosine']:
kde = KernelDensity(bandwidth, kernel=kernel).fit(X)
assert_raises(NotImplementedError, kde.sample, 100)
# non-regression test: used to return a scalar
X = rng.randn(4, 1)
kde = KernelDensity(kernel="gaussian").fit(X)
assert_equal(kde.sample().shape, (1, 1))
@pytest.mark.parametrize('algorithm', ['auto', 'ball_tree', 'kd_tree'])
@pytest.mark.parametrize('metric',
['euclidean', 'minkowski', 'manhattan',
'chebyshev', 'haversine'])
def test_kde_algorithm_metric_choice(algorithm, metric):
# Smoke test for various metrics and algorithms
rng = np.random.RandomState(0)
X = rng.randn(10, 2) # 2 features required for haversine dist.
Y = rng.randn(10, 2)
if algorithm == 'kd_tree' and metric not in KDTree.valid_metrics:
assert_raises(ValueError, KernelDensity,
algorithm=algorithm, metric=metric)
else:
kde = KernelDensity(algorithm=algorithm, metric=metric)
kde.fit(X)
y_dens = kde.score_samples(Y)
assert_equal(y_dens.shape, Y.shape[:1])
def test_kde_score(n_samples=100, n_features=3):
pass
# FIXME
# rng = np.random.RandomState(0)
# X = rng.random_sample((n_samples, n_features))
# Y = rng.random_sample((n_samples, n_features))
def test_kde_badargs():
assert_raises(ValueError, KernelDensity,
algorithm='blah')
assert_raises(ValueError, KernelDensity,
bandwidth=0)
assert_raises(ValueError, KernelDensity,
kernel='blah')
assert_raises(ValueError, KernelDensity,
metric='blah')
assert_raises(ValueError, KernelDensity,
algorithm='kd_tree', metric='blah')
kde = KernelDensity()
assert_raises(ValueError, kde.fit, np.random.random((200, 10)),
sample_weight=np.random.random((200, 10)))
assert_raises(ValueError, kde.fit, np.random.random((200, 10)),
sample_weight=-np.random.random(200))
def test_kde_pipeline_gridsearch():
# test that kde plays nice in pipelines and grid-searches
X, _ = make_blobs(cluster_std=.1, random_state=1,
centers=[[0, 1], [1, 0], [0, 0]])
pipe1 = make_pipeline(StandardScaler(with_mean=False, with_std=False),
KernelDensity(kernel="gaussian"))
params = dict(kerneldensity__bandwidth=[0.001, 0.01, 0.1, 1, 10])
search = GridSearchCV(pipe1, param_grid=params, cv=5)
search.fit(X)
assert_equal(search.best_params_['kerneldensity__bandwidth'], .1)
def test_kde_sample_weights():
n_samples = 400
size_test = 20
weights_neutral = np.full(n_samples, 3.)
for d in [1, 2, 10]:
rng = np.random.RandomState(0)
X = rng.rand(n_samples, d)
weights = 1 + (10 * X.sum(axis=1)).astype(np.int8)
X_repetitions = np.repeat(X, weights, axis=0)
n_samples_test = size_test // d
test_points = rng.rand(n_samples_test, d)
for algorithm in ['auto', 'ball_tree', 'kd_tree']:
for metric in ['euclidean', 'minkowski', 'manhattan',
'chebyshev']:
if algorithm != 'kd_tree' or metric in KDTree.valid_metrics:
kde = KernelDensity(algorithm=algorithm, metric=metric)
# Test that adding a constant sample weight has no effect
kde.fit(X, sample_weight=weights_neutral)
scores_const_weight = kde.score_samples(test_points)
sample_const_weight = kde.sample(random_state=1234)
kde.fit(X)
scores_no_weight = kde.score_samples(test_points)
sample_no_weight = kde.sample(random_state=1234)
assert_allclose(scores_const_weight, scores_no_weight)
assert_allclose(sample_const_weight, sample_no_weight)
# Test equivalence between sampling and (integer) weights
kde.fit(X, sample_weight=weights)
scores_weight = kde.score_samples(test_points)
sample_weight = kde.sample(random_state=1234)
kde.fit(X_repetitions)
scores_ref_sampling = kde.score_samples(test_points)
sample_ref_sampling = kde.sample(random_state=1234)
assert_allclose(scores_weight, scores_ref_sampling)
assert_allclose(sample_weight, sample_ref_sampling)
# Test that sample weights has a non-trivial effect
diff = np.max(np.abs(scores_no_weight - scores_weight))
assert diff > 0.001
# Test invariance with respect to arbitrary scaling
scale_factor = rng.rand()
kde.fit(X, sample_weight=(scale_factor * weights))
scores_scaled_weight = kde.score_samples(test_points)
assert_allclose(scores_scaled_weight, scores_weight)
def test_pickling(tmpdir):
# Make sure that predictions are the same before and after pickling. Used
# to be a bug because sample_weights wasn't pickled and the resulting tree
# would miss some info.
kde = KernelDensity()
data = np.reshape([1., 2., 3.], (-1, 1))
kde.fit(data)
X = np.reshape([1.1, 2.1], (-1, 1))
scores = kde.score_samples(X)
file_path = str(tmpdir.join('dump.pkl'))
_joblib.dump(kde, file_path)
kde = _joblib.load(file_path)
scores_pickled = kde.score_samples(X)
assert_allclose(scores, scores_pickled)
|
