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
|
#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
from openturns.usecases import ishigami_function
ot.TESTPREAMBLE()
ot.RandomGenerator.SetSeed(0)
# Ishigami use-case
ishigami = ishigami_function.IshigamiModel()
distX = ishigami.distribution
# Get a sample of it
size = 100
X = distX.getSample(size)
# The Ishigami model
modelIshigami = ishigami.model
modelIshigami.setParameter([5, 0.1])
# Apply model: Y = m(X)
Y = modelIshigami(X)
# We define the covariance models for the HSIC indices.
# For the input, we consider a SquaredExponential covariance model.
covarianceModelCollection = ot.CovarianceModelCollection()
# Input sample
for i in range(3):
Xi = X.getMarginal(i)
Cov = ot.SquaredExponential(1)
Cov.setScale(Xi.computeStandardDeviation())
covarianceModelCollection.add(Cov)
# Output sample with squared exponential covariance
Cov2 = ot.SquaredExponential(1)
Cov2.setScale(Y.computeStandardDeviation())
covarianceModelCollection.add(Cov2)
# We choose an estimator type :
# - unbiased: HSICUStat;
# - biased: HSICVStat.
#
estimatorType = ot.HSICUStat()
# random generator state
# use the same state for parallel/sequential validation
state = ot.RandomGenerator.GetState()
for key in [True, False]:
ot.ResourceMap.SetAsBool("HSICEstimator-ParallelPValues", key)
ot.RandomGenerator.SetState(state)
# We eventually build the HSIC object!
hsic = ot.HSICEstimatorGlobalSensitivity(
covarianceModelCollection, X, Y, estimatorType
)
# We get the HSIC indices
HSICIndices = hsic.getHSICIndices()
ott.assert_almost_equal(HSICIndices, [0.02228377, 0.00025668, 0.00599247])
# and the R2-HSIC
R2HSIC = hsic.getR2HSICIndices()
ott.assert_almost_equal(R2HSIC, [0.29807297, 0.00344498, 0.07726572])
# We set the bootstrap size for the pvalue estimate
b = 1000
hsic.setPermutationSize(b)
# We get the pvalue estimate by permutations
pvaluesPerm = hsic.getPValuesPermutation()
ott.assert_almost_equal(pvaluesPerm, [0.00000000, 0.29670330, 0.00199800])
pvaluesAs = hsic.getPValuesAsymptotic()
ott.assert_almost_equal(pvaluesAs, [0.00000000, 0.33271992, 0.00165620])
# thread-safety issue in DiracCovarianceModel
for key in [True, False]:
ot.ResourceMap.SetAsBool("DiracCovarianceModel-CheckUnique", key)
n = 20
x = ot.Sample(n, 1)
y = ot.Sample(n, 1)
covs = [ot.DiracCovarianceModel()] * 2
for i in range(10000):
globHSIC = ot.HSICEstimatorGlobalSensitivity(covs, x, y, ot.HSICVStat())
|
