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

Methods

`analyticalValidation`()	Whether an analytical validation is requested.
`asPythonPhysicalModel`(study)	Create a Python model wrapping the metamodel created by the analysis.
`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.
`getInteraction`()	Accessor to the interaction flag.
`getInterestVariables`()	Get the variables to analyse.
`getKFoldValidationNumberOfFolds`()	Number of folds accessor.
`getKFoldValidationSeed`()	Seed accessor.
`getMetaModel`()	metamodel accessor.
`getName`()	Accessor to the object's name.
`getPythonScript`()	Physical model accessor.
`getResult`()	Results accessor.
`getTestSampleValidationPercentageOfPoints`()	Percentage of points accessor.
`getTestSampleValidationSeed`()	Seed accessor.
`getWarningMessage`()	Warning message accessor.
`hasName`()	Test if the object is named.
`hasValidResult`()	Whether the analysis has been run.
`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.
`setTestSampleValidation`(validation)	Whether a validation with a test sample is requested.
`setTestSampleValidationPercentageOfPoints`(...)	Percentage of points accessor.
`setTestSampleValidationSeed`(seed)	Seed accessor.
`testSampleValidation`()	Whether a validation with a test sample is requested.

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()

__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.

asPythonPhysicalModel(study)¶

Create a Python model wrapping the metamodel created by the analysis.

Parameters:

studyStudy: The study to which the analysis belong

Returns:

modelPythonPhysicalModel: The python model

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

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

getMetaModel()¶

metamodel accessor.

Returns:

metamodelPhysicalModel: The metamodel created by the analysis

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

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

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

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.

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

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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