MetaModelValidation¶

class MetaModelValidation(*args)¶

Base class to score a metamodel and perform validations.

Refer to Cross validation assessment of PC models.

Parameters:

inputValidationSample, outputValidationSample2-d sequence of float: The input and output validation samples, not used during the learning step.
metaModelFunction: Metamodel to validate.

Notes

A MetaModelValidation object is used for the validation process of a metamodel. For that purpose, a dataset independent of the learning step, is used to score the surrogate model. Its main functionalities are :

To compute the predictivity factor $Q_2$
To get the residual sample, its non parametric distribution
To draw a model vs metamodel validation graph.

Currently only one dimensional output models are available.

Examples

>>> import openturns as ot
>>> from math import pi
>>> dist = ot.Uniform(-pi/2, pi/2)
>>> # Model here is sin(x)
>>> model = ot.SymbolicFunction(['x'], ['sin(x)'])
>>> # We can build several types of models (kriging, pc, ...)
>>> # We use a Taylor development (order 5) and compare the metamodel with the model
>>> metaModel = ot.SymbolicFunction(['x'], ['x - x^3/6.0 + x^5/120.0'])
>>> x = dist.getSample(10)
>>> y = model(x)
>>> # Validation of the model
>>> val = ot.MetaModelValidation(x, y, metaModel)
>>> # Compute the first indicator : q2
>>> q2 = val.computePredictivityFactor()
>>> # Get the residual
>>> residual = val.getResidualSample()
>>> # Get the histogram of residual
>>> histoResidual = val.getResidualDistribution(False)
>>> # Draw the validation graph
>>> graph = val.drawValidation()

Methods

`computePredictivityFactor`()	Compute the predictivity factor.
`drawValidation`()	Plot a model vs metamodel graph for visual validation.
`getClassName`()	Accessor to the object's name.
`getId`()	Accessor to the object's id.
`getInputSample`()	Accessor to the input sample.
`getName`()	Accessor to the object's name.
`getOutputSample`()	Accessor to the output sample.
`getResidualDistribution`([smooth])	Compute the non parametric distribution of the residual sample.
`getResidualSample`()	Compute the residual sample.
`getShadowedId`()	Accessor to the object's shadowed id.
`getVisibility`()	Accessor to the object's visibility state.
`hasName`()	Test if the object is named.
`hasVisibleName`()	Test if the object has a distinguishable name.
`setName`(name)	Accessor to the object's name.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setVisibility`(visible)	Accessor to the object's visibility state.

__init__(*args)¶

computePredictivityFactor()¶

Compute the predictivity factor.

Returns:

q2Point: The predictivity factor

Notes

The predictivity factor $Q_2$ is given by :

$Q_2 = 1 - \frac{\sum_{l=1}^{N} (Y_{l} -\hat{f}(X_l))^2}{N \cdot Var(Y)}$

drawValidation()¶

Plot a model vs metamodel graph for visual validation.

Returns:

graphGridLayout: The visual validation graph.

getClassName()¶

Accessor to the object’s name.

Returns:

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

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getInputSample()¶

Accessor to the input sample.

Returns:

inputSampleSample: Input sample of a model evaluated apart.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getOutputSample()¶

Accessor to the output sample.

Returns:

outputSampleSample: Output sample of a model evaluated apart.

getResidualDistribution(smooth=True)¶

Compute the non parametric distribution of the residual sample.

Parameters:

smoothbool: Tells if distribution is smooth (true) or not. Default argument is true.

Returns:

residualDistributionDistribution: The residual distribution.

Notes

The residual distribution is built thanks to KernelSmoothing if smooth argument is true. Otherwise, an histogram distribution is returned, thanks to HistogramFactory.

getResidualSample()¶

Compute the residual sample.

Returns: