HSICEstimatorGlobalSensitivity

class HSICEstimatorGlobalSensitivity(*args)

Implement a HSIC estimator for global analysis.

Parameters

covarianceModelCollectionlist of CovarianceModel

List of all covariance kernels. The first kernels are linked to the input and the last one is for the output.

X2-d sequence of float

The input sample used for the HSIC analysis of dimension .

Y2-d sequence of float

The output sample used for the HSIC analysis of dimension 1.

estimatorTypeHSICStat

An estimator for internal computations.

See also

HSICEstimatorConditionalSensitivity, HSICEstimatorTargetSensitivity

Examples

>>> import openturns as ot
>>> from math import pi

Generate input and output samples.

>>> # 3d input distribution with an independent copula
>>> distX = ot.ComposedDistribution([ot.Uniform(-pi, pi)] * 3)
>>> X = distX.getSample(100) # get a sample
>>>
>>> # Apply the Ishigami model.
>>> inputs = ['X1', 'X2', 'X3']
>>> formula = ['sin(X1) + 5.0 * (sin(X2))^2 + 0.1 * X3^4 * sin(X1)']
>>> modelIshigami = ot.SymbolicFunction(inputs, formula)
>>> Y = modelIshigami(X) # Y = modelIshigami(X)

Define covariance kernels for the model inputs. Put them in a list.

>>> covarianceModelCollection = []
>>> for i in range(3):
...     Xi = X.getMarginal(i)
...     Cov = ot.SquaredExponential(1)
...     Cov.setScale(Xi.computeStandardDeviation())
...     covarianceModelCollection.append(Cov)

Append the list with the covariance kernel for the model output.

>>> covarianceModelCollection.append(ot.SquaredExponential(Y.computeStandardDeviation()))

Choose the statistic that will be used to estimate the HSIC indices.

>>> estimatorType = ot.HSICUStat() # could be HSICVStat instead

Build and use the HSIC estimator for global sensitivity analysis.

>>> hsic = ot.HSICEstimatorGlobalSensitivity(covarianceModelCollection, X, Y, estimatorType)
>>> print(hsic.getR2HSICIndices())
[0.404051,0.0206756,0.0846069]

Methods

drawHSICIndices()	Draw the HSIC indices.
drawPValuesAsymptotic()	Draw the p-values obtained with an asymptotic formula.
drawPValuesPermutation()	Draw the p-values obtained by permutation.
drawR2HSICIndices()	Draw the R2-HSIC indices.
getClassName()	Accessor to the object's name.
getCovarianceModelCollection()	Get the list of all covariance models used.
getDimension()	Get the dimension of the input sample.
getEstimator()	Get the estimator used for computations.
getHSICIndices()	Get the HSIC indices.
getId()	Accessor to the object's id.
getInputSample()	Get the input sample.
getName()	Accessor to the object's name.
getOutputSample()	Get the output sample.
getPValuesAsymptotic()	Get the p-values obtained with an asymptotic formula.
getPValuesPermutation()	Get the p-value estimated through permutations.
getPermutationSize()	Get the number of permutations.
getR2HSICIndices()	Get the R2-HSIC indices.
getShadowedId()	Accessor to the object's shadowed id.
getSize()	Get the size of the input sample.
getVisibility()	Accessor to the object's visibility state.
hasName()	Test if the object is named.
hasVisibleName()	Test if the object has a distinguishable name.
run()	Compute all values at once.
setCovarianceModelCollection(coll)	Set the covariance models.
setInputSample(inputSample)	Set the input sample.
setName(name)	Accessor to the object's name.
setOutputSample(outputSample)	Set the output sample.
setPermutationSize(B)	Set the number of permutations to be used for p-value estimate.
setShadowedId(id)	Accessor to the object's shadowed id.
setVisibility(visible)	Accessor to the object's visibility state.

__init__(*args)

drawHSICIndices()

Draw the HSIC indices.

Returns

graphGraph

The graph of all HSIC indices according to components.

drawPValuesAsymptotic()

Draw the p-values obtained with an asymptotic formula.

Returns

graphGraph

The graph of all p-values estimated with an asymptotic formula.

drawPValuesPermutation()

Draw the p-values obtained by permutation.

Returns

graphGraph

The graph of all p-values by permutation according to components.

drawR2HSICIndices()

Draw the R2-HSIC indices.

Returns

graphGraph

The graph of all R2-HSIC indices according to components.

getClassName()

Accessor to the object’s name.

Returns

class_namestr

The object class name (object.__class__.__name__).

getCovarianceModelCollection()

Get the list of all covariance models used.

Returns

collCovarianceModelCollection

The list of all covariance models used. The last one is the output covariance model.

getDimension()

Get the dimension of the input sample.

Returns

dimint

The dimension of the input sample.

getEstimator()

Get the estimator used for computations.

Returns

estimatorHSICStat

The estimator used for internal computations.

getHSICIndices()

Get the HSIC indices.

Returns

hsicIndicesPoint

The HSIC indices of all components.

getId()

Accessor to the object’s id.

Returns

idint

Internal unique identifier.

getInputSample()

Get the input sample.

Returns

inSampleSample

The input sample used for analysis.

getName()

Accessor to the object’s name.

Returns

namestr

The name of the object.

getOutputSample()

Get the output sample.

Returns

outSampleSample

The output sample used for analysis.

getPValuesAsymptotic()

Get the p-values obtained with an asymptotic formula.

Returns

pvalsequence of float

The p-values for all components.

getPValuesPermutation()

Get the p-value estimated through permutations.

Returns

pvalPoint

The p-values of all components estimated with permutations of the data.

getPermutationSize()

Get the number of permutations.

Returns

permutationSizeint

The number of permutations.

getR2HSICIndices()

Get the R2-HSIC indices.

Returns

r2hsicIndicesPoint

The R2-HSIC indices of all components.

getShadowedId()

Accessor to the object’s shadowed id.

Returns

idint

Internal unique identifier.

getSize()

Get the size of the input sample.

Returns

sizeint

The size of the input sample.

getVisibility()

Accessor to the object’s visibility state.

Returns

visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns

hasNamebool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns

hasVisibleNamebool

True if the name is not empty and not the default one.

run()

Compute all values at once.

setCovarianceModelCollection(coll)

Set the covariance models.

Parameters

collCovarianceModelCollection

The list of all covariance models.

setInputSample(inputSample)

Set the input sample.

Parameters

inputSample2-d sequence of float

The input sample to be used.

setName(name)

Accessor to the object’s name.

Parameters

namestr

The name of the object.

setOutputSample(outputSample)

Set the output sample.

Parameters

outputSample2-d sequence of float

The output sample to be used.

setPermutationSize(B)

Set the number of permutations to be used for p-value estimate.

Parameters

Bint

The number of permutation used for p-value estimates.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters

idint

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters

visiblebool

Visibility flag.