HSICEstimatorConditionalSensitivity¶

class HSICEstimatorConditionalSensitivity(*args)¶

Implement a HSIC estimator for conditional analysis.

Parameters:

covarianceModelCollectionlist of CovarianceModel: List of all covariance kernels. The $d$ 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 $d$ .
Y2-d sequence of float: The output sample used for the HSIC analysis of dimension 1.
weightFunctionFunction: A weight function used for the inputs.

See also

HSICEstimatorGlobalSensitivity, HSICEstimatorTargetSensitivity

Notes

Conditional sensitivity analysis relies on the HSICVStat estimator.

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()))

To perform sensititivity analysis under the condition that the output belongs or is near a domain, define a weight function based on the distance to this domain.

>>> dist = ot.DistanceToDomainFunction(ot.Interval(5, float('inf')))
>>> func = ot.SymbolicFunction('x', 'exp(-0.5 * x)')
>>> weight = ot.ComposedFunction(func, dist)

Build and use the HSIC estimator for conditional sensitivity analysis.

>>> hsic = ot.HSICEstimatorConditionalSensitivity(covarianceModelCollection, X, Y, weight)
>>> print(hsic.getR2HSICIndices())
[0.280788,0.00600014,0.0577616]

Methods

`drawHSICIndices`()	Draw the HSIC indices.
`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.
`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.
`getWeightFunction`()	Get the weight function used.
`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.
`setWeightFunction`(weightFunction)	Set the weight function.

__init__(*args)¶

drawHSICIndices()¶

Draw the HSIC indices.

Returns:

graphGraph: The graph of all HSIC indices according to components.

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.

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.

getWeightFunction()¶

Get the weight function used.

Returns:

weightFunctionFunction: The weight function used for the conditional estimator.

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.

setWeightFunction(weightFunction)¶

Set the weight function.

Parameters:

weightFunctionFunction: The weight function used for the conditional estimator.

Examples using the class¶

The HSIC sensitivity indices: the Ishigami model

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HSICEstimatorConditionalSensitivity¶

Examples using the class¶