PolynomialRegressionAnalysis¶

class persalys.PolynomialRegressionAnalysis(*args)¶

Polynomial stepwise regression.

Allows one to select of the most suitable polynomial (canonical) basis for a linear regression model with the help of the stepwise algorithm.

See also LinearModelStepwiseAlgorithm.

Parameters:

namestr: Name
designOfExperimentDesignOfExperiment: Design of experiments

Examples

Create the model:

>>> import openturns as ot
>>> import persalys
>>> from math import pi
>>> ot.RandomGenerator.SetSeed(0)

Create the model:

>>> xi1 = persalys.Input('xi1', ot.Uniform(-pi, pi))
>>> xi2 = persalys.Input('xi2', ot.Uniform(-pi, pi))
>>> xi3 = persalys.Input('xi3', ot.Uniform(-pi, pi))
>>> y0 = persalys.Output('y0')
>>> myPhysicalModel = persalys.SymbolicPhysicalModel('myPhysicalModel', [xi1, xi2, xi3], [y0], ['sin(xi1) + 7. * (sin(xi2)) ^ 2 + 0.1 * xi3^4 * sin(xi1)'])

Create the design of experiments:

>>> aDesign = persalys.ProbabilisticDesignOfExperiment('aDesign', myPhysicalModel, 100, 'LHS')
>>> aDesign.run()

Create the linear regression analysis:

>>> lm = persalys.PolynomialRegressionAnalysis('lm', aDesign)
>>> lm.setDegree(1)
>>> lm.setInteraction(False)
>>> lm.run()

Get the result:

>>> result = lm.getResult()

Methods

`analyticalValidation`()	Whether an analytical validation is requested.
`getClassName`()	Accessor to the object's name.
`getDegree`()	Accessor to the basis degree.
`getDesignOfExperiment`()	Design of experiments accessor.
`getEffectiveInputSample`()	Effective input sample accessor.
`getEffectiveOutputSample`()	Effective output sample accessor.
`getErrorMessage`()	Error message accessor.
`getId`()	Accessor to the object's id.
`getInteraction`()	Accessor to the interaction flag.
`getInterestVariables`()	Get the variables to analyse.
`getKFoldValidationNumberOfFolds`()	Number of folds accessor.
`getKFoldValidationSeed`()	Seed accessor.
`getName`()	Accessor to the object's name.
`getPythonScript`()	Physical model accessor.
`getResult`()	Results accessor.
`getShadowedId`()	Accessor to the object's shadowed id.
`getTestSampleValidationPercentageOfPoints`()	Percentage of points accessor.
`getTestSampleValidationSeed`()	Seed accessor.
`getVisibility`()	Accessor to the object's visibility state.
`getWarningMessage`()	Warning message accessor.
`hasName`()	Test if the object is named.
`hasValidResult`()	Whether the analysis has been run.
`hasVisibleName`()	Test if the object has a distinguishable name.
`isReliabilityAnalysis`()	Whether the analysis involves reliability.
`isRunning`()	Whether the analysis is running.
`kFoldValidation`()	Whether a k-Fold cross-validation is requested.
`leaveOneOutValidation`()	Whether a validation by leave-one-out is requested.
`run`()	Launch the analysis.
`setAnalyticalValidation`(validation)	Whether an analytical validation is requested.
`setDegree`(degree)	Accessor to the basis degree.
`setInteraction`(interaction)	Accessor to the interaction flag.
`setInterestVariables`(variablesNames)	Set the variables to analyse.
`setKFoldValidation`(validation)	Whether a k-Fold cross-validation is requested.
`setKFoldValidationNumberOfFolds`(nbFolds)	Number of folds accessor.
`setKFoldValidationSeed`(seed)	Seed accessor.
`setLeaveOneOutValidation`(validation)	Whether it is sparse.
`setName`(name)	Accessor to the object's name.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setTestSampleValidation`(validation)	Whether a validation with a test sample is requested.
`setTestSampleValidationPercentageOfPoints`(...)	Percentage of points accessor.
`setTestSampleValidationSeed`(seed)	Seed accessor.
`setVisibility`(visible)	Accessor to the object's visibility state.
`testSampleValidation`()	Whether a validation with a test sample is requested.

canBeLaunched
getElapsedTime
getParentObserver

__init__(*args)¶

analyticalValidation()¶

Whether an analytical validation is requested.

Returns:

validationbool: Whether an analytical validation is requested. This method corresponds to an approximation of the Leave-one-out method result.

getClassName()¶

Accessor to the object’s name.

Returns:

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

getDegree()¶

Accessor to the basis degree.

Returns:

degresint: Basis degree

getDesignOfExperiment()¶

Design of experiments accessor.

Returns:

modelDesignOfExperiment: Design of experiments

getEffectiveInputSample()¶

Effective input sample accessor.

Returns:

sampleopenturns.Sample: Sample of all the input variables if all of them are deterministic. Otherwise, sample of the stochastic input variables.

getEffectiveOutputSample()¶

Effective output sample accessor.

Returns:

sampleopenturns.Sample: Sample of the interest output variables.

getErrorMessage()¶

Error message accessor.

Returns:

messagestr: Error message if the analysis failed

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getInteraction()¶

Accessor to the interaction flag.

Returns:

interactionbool: Whether to include interaction terms in the basis

getInterestVariables()¶

Get the variables to analyse.

Returns:

variablesNamessequence of str: Names of the variables to analyse

getKFoldValidationNumberOfFolds()¶

Number of folds accessor.

Returns:

foldsint: Number of folds. By default it is 3.

getKFoldValidationSeed()¶

Seed accessor.

Returns:

seedint: Seed value for k-Fold cross-validation

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getPythonScript()¶

Physical model accessor.

Returns:

scriptstr: Python script to replay the analysis

getResult()¶

Results accessor.

Returns:

resultPolynomialRegressionAnalysisResult: Results

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

getTestSampleValidationPercentageOfPoints()¶

Percentage of points accessor.

Returns:

percentageint: Percentage of points used to validate the metamodel. By default it is 20%.

getTestSampleValidationSeed()¶

Seed accessor.

Returns:

seedint: Seed value for the validation with a test sample

getVisibility()¶

Accessor to the object’s visibility state.

Returns:

visiblebool: Visibility flag.

getWarningMessage()¶

Warning message accessor.

Returns:

messagestr: Warning message which can appear during the analysis computation

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasValidResult()¶

Whether the analysis has been run.

Returns:

hasValidResultbool: Whether the analysis has already been run

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns:

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

isReliabilityAnalysis()¶

Whether the analysis involves reliability.

Returns:

isReliabilityAnalysisbool: Whether the analysis involves a reliability analysis

isRunning()¶

Whether the analysis is running.

Returns:

isRunningbool: Whether the analysis is running

kFoldValidation()¶

Whether a k-Fold cross-validation is requested.

Returns:

validationbool: Whether a k-Fold cross-validation is requested

leaveOneOutValidation()¶

Whether a validation by leave-one-out is requested.

Returns:

validationbool: Whether a validation by leave-one-out is requested

run()¶: Launch the analysis.

setAnalyticalValidation(validation)¶

Whether an analytical validation is requested.

Parameters:

validationbool: Whether an analytical validation is requested. This method corresponds to an approximation of the Leave-one-out method result.

setDegree(degree)¶

Accessor to the basis degree.

Parameters:

degresint: Basis degree

setInteraction(interaction)¶

Accessor to the interaction flag.

Parameters:

interactionbool: Whether to include interaction terms in the basis

setInterestVariables(variablesNames)¶

Set the variables to analyse.

Parameters:

variablesNamessequence of str: Names of the variables to analyse

setKFoldValidation(validation)¶

Whether a k-Fold cross-validation is requested.

Parameters:

validationbool: Whether a k-Fold cross-validation is requested

setKFoldValidationNumberOfFolds(nbFolds)¶

Number of folds accessor.

Parameters:

foldsint: Number of folds. By default it is 3.

setKFoldValidationSeed(seed)¶

Seed accessor.

Parameters:

seedint: Seed value for k-Fold cross-validation

setLeaveOneOutValidation(validation)¶

Whether it is sparse.

Parameters:

validationbool: Whether a validation by leave-one-out is requested

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters:

idint: Internal unique identifier.

setTestSampleValidation(validation)¶

Whether a validation with a test sample is requested.

Parameters:

validationbool: Whether a validation with a test sample is requested. The data sample is dividing into two sub-samples: a training sample (default: 80% of the sample points) and a test sample (default: 20% of the sample points). A new metamodel is built with the training sample and is validated with the test sample. The points are randomly picked in the data sample (by default the seed is 1).

setTestSampleValidationPercentageOfPoints(percentage)¶

Percentage of points accessor.

Parameters:

percentageint: Percentage of points used to validate the metamodel. By default it is 20%.

setTestSampleValidationSeed(seed)¶

Seed accessor.

Parameters:

seedint: Seed value for the validation with a test sample

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters:

visiblebool: Visibility flag.

testSampleValidation()¶

Whether a validation with a test sample is requested.

Returns:

validationbool: Whether a validation with a test sample is requested. The data sample is dividing into two sub-samples: a training sample (default: 80% of the sample points) and a test sample (default: 20% of the sample points). A new metamodel is built with the training sample and is validated with the test sample. The points are randomly picked in the data sample (by default the seed is 1).

PolynomialRegressionAnalysis¶

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