ExpertMixture¶

class ExpertMixture(*args)¶

Expert mixture defining a piecewise function according to a classifier.

This implements an expert mixture which is a piecewise function $f$ defined by the collection of functions $(f_i)_{i=1, \ldots, N}$ given in basis and according to a classifier:

$f(\vect{x}) &= f_1(\vect{x}) \hspace{1em} \forall \vect{z} \in \text{Class} 1 \\ &= f_k(\vect{x}) \hspace{1em} \forall \vect{z} \in \text{Class} k \\ &= f_N(\vect{x}) \hspace{1em} \forall \vect{z} \in \text{Class} N$

where the $N$ classes are defined by the classifier.

In supervised mode the classifier partitions the input and output space at once:

$\vect{z} = (\vect{x}, f(\vect{x}))$

whereas in non-supervised mode only the input space is partitioned:

$\vect{z} = \vect{x}$

Parameters:

basissequence of Function: A basis
classifierClassifier: A classifier
supervisedbool (default=True): In supervised mode, the classifier partitions the space of $(\vect(x), f(\vect(x)))$ whereas in non-supervised mode the classifier only partitions the input space.

See also

Classifier, MixtureClassifier

Notes

The number of experts must match the number of classes of the classifier.

Examples

>>> import openturns as ot
>>> R = ot.CorrelationMatrix(2)
>>> R[0, 1] = -0.99
>>> d1 = ot.Normal([-1.0, 1.0], [1.0, 1.0], R)
>>> R[0, 1] = 0.99
>>> d2 = ot.Normal([1.0, 1.0], [1.0, 1.0], R)
>>> distribution = ot.Mixture([d1, d2], [1.0]*2)
>>> classifier = ot.MixtureClassifier(distribution)
>>> f1 = ot.SymbolicFunction(['x'], ['-x'])
>>> f2 = ot.SymbolicFunction(['x'], ['x'])
>>> experts = [f1, f2]
>>> evaluation = ot.ExpertMixture(experts, classifier)
>>> moe = ot.Function(evaluation)
>>> print(moe([-0.3]))
[0.3]
>>> print(moe([0.1]))
[0.1]

Methods

`__call__`(*args)	Call self as a function.
`draw`(*args)	Draw the output of function as a `Graph`.
`getCallsNumber`()	Accessor to the number of times the function has been called.
`getCheckOutput`()	Accessor to the output verification flag.
`getClassName`()	Accessor to the object's name.
`getClassifier`()	Accessor the classifier.
`getDescription`()	Accessor to the description of the inputs and outputs.
`getExperts`()	Accessor the basis.
`getId`()	Accessor to the object's id.
`getInputDescription`()	Accessor to the description of the inputs.
`getInputDimension`()	Accessor to the number of the inputs.
`getMarginal`(*args)	Accessor to marginal.
`getName`()	Accessor to the object's name.
`getOutputDescription`()	Accessor to the description of the outputs.
`getOutputDimension`()	Accessor to the number of the outputs.
`getParameter`()	Accessor to the parameter values.
`getParameterDescription`()	Accessor to the parameter description.
`getParameterDimension`()	Accessor to the dimension of the parameter.
`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.
`isActualImplementation`()	Accessor to the validity flag.
`isLinear`()	Accessor to the linearity of the evaluation.
`isLinearlyDependent`(index)	Accessor to the linearity of the evaluation with regard to a specific variable.
`parameterGradient`(inP)	Gradient against the parameters.
`setCheckOutput`(checkOutput)	Accessor to the output verification flag.
`setClassifier`(classifier)	Accessor the classifier.
`setDescription`(description)	Accessor to the description of the inputs and outputs.
`setExperts`(experts)	Accessor the basis.
`setInputDescription`(inputDescription)	Accessor to the description of the inputs.
`setName`(name)	Accessor to the object's name.
`setOutputDescription`(outputDescription)	Accessor to the description of the outputs.
`setParameter`(parameters)	Accessor to the parameter values.
`setParameterDescription`(description)	Accessor to the parameter description.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setVisibility`(visible)	Accessor to the object's visibility state.

__init__(*args)¶

draw(*args)¶

Draw the output of function as a Graph.

Available usages:

draw(inputMarg, outputMarg, CP, xiMin, xiMax, ptNb)

draw(firstInputMarg, secondInputMarg, outputMarg, CP, xiMin_xjMin, xiMax_xjMax, ptNbs)

draw(xiMin, xiMax, ptNb)

draw(xiMin_xjMin, xiMax_xjMax, ptNbs)

Parameters:

outputMarg, inputMargint, $outputMarg, inputMarg \geq 0$: outputMarg is the index of the marginal to draw as a function of the marginal with index inputMarg.
firstInputMarg, secondInputMargint, $firstInputMarg, secondInputMarg \geq 0$: In the 2D case, the marginal outputMarg is drawn as a function of the two marginals with indexes firstInputMarg and secondInputMarg.
CPsequence of float: Central point.
xiMin, xiMaxfloat: Define the interval where the curve is plotted.
xiMin_xjMin, xiMax_xjMaxsequence of float of dimension 2.: In the 2D case, define the intervals where the curves are plotted.
ptNbint $ptNb > 0$ or list of ints of dimension 2 $ptNb_k > 0, k=1,2$: The number of points to draw the curves.

Notes

We note $f: \Rset^n \rightarrow \Rset^p$ where $\vect{x} = (x_1, \dots, x_n)$ and $f(\vect{x}) = (f_1(\vect{x}), \dots,f_p(\vect{x}))$ , with $n\geq 1$ and $p\geq 1$ .

In the first usage:

Draws graph of the given 1D outputMarg marginal $f_k: \Rset^n \rightarrow \Rset$ as a function of the given 1D inputMarg marginal with respect to the variation of $x_i$ in the interval $[x_i^{min}, x_i^{max}]$ , when all the other components of $\vect{x}$ are fixed to the corresponding ones of the central point CP. Then it draws the graph: $t\in [x_i^{min}, x_i^{max}] \mapsto f_k(CP_1, \dots, CP_{i-1}, t, CP_{i+1} \dots, CP_n)$ .

In the second usage:

Draws the iso-curves of the given outputMarg marginal $f_k$ as a function of the given 2D firstInputMarg and secondInputMarg marginals with respect to the variation of $(x_i, x_j)$ in the interval $[x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}]$ , when all the other components of $\vect{x}$ are fixed to the corresponding ones of the central point CP. Then it draws the graph: $(t,u) \in [x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}] \mapsto f_k(CP_1, \dots, CP_{i-1}, t, CP_{i+1}, \dots, CP_{j-1}, u, CP_{j+1} \dots, CP_n)$ .

In the third usage:

The same as the first usage but only for function $f: \Rset \rightarrow \Rset$ .

In the fourth usage:

The same as the second usage but only for function $f: \Rset^2 \rightarrow \Rset$ .

Examples

>>> import openturns as ot
>>> from openturns.viewer import View
>>> f = ot.SymbolicFunction(['x'], ['sin(2*pi_*x)*exp(-x^2/2)'])
>>> graph = f.draw(-1.2, 1.2, 100)
>>> View(graph).show()

getCallsNumber()¶

Accessor to the number of times the function has been called.

Returns:

calls_numberint: Integer that counts the number of times the function has been called since its creation.

getCheckOutput()¶

Accessor to the output verification flag.

Returns:

check_outputbool: Whether to check return values for nan or inf.

getClassName()¶

Accessor to the object’s name.

Returns:

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

getClassifier()¶

Accessor the classifier.

Returns:

classifierClassifier: The classifier.

getDescription()¶

Accessor to the description of the inputs and outputs.

Returns:

descriptionDescription: Description of the inputs and the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y0]

getExperts()¶

Accessor the basis.

Returns:

basiscollection of Function: The collection of functions $(f_i)_{i=1, \ldots, N}$ .

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getInputDescription()¶

Accessor to the description of the inputs.

Returns:

descriptionDescription: Description of the inputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getInputDescription())
[x1,x2]

getInputDimension()¶

Accessor to the number of the inputs.

Returns:

number_inputsint: Number of inputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getInputDimension())
2

getMarginal(*args)¶

Accessor to marginal.

Parameters:

indicesint or list of ints: Set of indices for which the marginal is extracted.

Returns:

marginalFunction: Function corresponding to either $f_i$ or $(f_i)_{i \in indices}$ , with $f:\Rset^n \rightarrow \Rset^p$ and $f=(f_0 , \dots, f_{p-1})$ .

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getOutputDescription()¶

Accessor to the description of the outputs.

Returns:

descriptionDescription: Description of the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getOutputDescription())
[y0]

getOutputDimension()¶

Accessor to the number of the outputs.

Returns:

number_outputsint: Number of outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getOutputDimension())
1

getParameter()¶

Accessor to the parameter values.

Returns:

parameterPoint: The parameter values.

getParameterDescription()¶

Accessor to the parameter description.

Returns:

parameterDescription: The parameter description.

getParameterDimension()¶

Accessor to the dimension of the parameter.

Returns:

parameter_dimensionint: Dimension of the parameter.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

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.

isActualImplementation()¶

Accessor to the validity flag.

Returns:

is_implbool: Whether the implementation is valid.

isLinear()¶

Accessor to the linearity of the evaluation.

Returns:

linearbool: True if the evaluation is linear, False otherwise.

isLinearlyDependent(index)¶

Accessor to the linearity of the evaluation with regard to a specific variable.

Parameters:

indexint: The index of the variable with regard to which linearity is evaluated.

Returns:

linearbool: True if the evaluation is linearly dependent on the specified variable, False otherwise.

parameterGradient(inP)¶

Gradient against the parameters.

Parameters:

xsequence of float: Input point

Returns:

parameter_gradientMatrix: The parameters gradient computed at x.

setCheckOutput(checkOutput)¶

Accessor to the output verification flag.

Parameters:

check_outputbool: Whether to check return values for nan or inf.

setClassifier(classifier)¶

Accessor the classifier.

Parameters:

classifierClassifier: The classifier.

setDescription(description)¶

Accessor to the description of the inputs and outputs.

Parameters:

descriptionsequence of str: Description of the inputs and the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y0]
>>> f.setDescription(['a','b','y'])
>>> print(f.getDescription())
[a,b,y]

setExperts(experts)¶

Accessor the basis.

Parameters:

basisBasis: The collection of functions $(f_i)_{i=1, \ldots, N}$ .

setInputDescription(inputDescription)¶

Accessor to the description of the inputs.

Returns:

descriptionDescription: Description of the inputs.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setOutputDescription(outputDescription)¶

Accessor to the description of the outputs.

Returns:

descriptionDescription: Description of the outputs.

setParameter(parameters)¶

Accessor to the parameter values.

Parameters:

parametersequence of float: The parameter values.

setParameterDescription(description)¶

Accessor to the parameter description.

Parameters:

parameterDescription: The parameter description.

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.

Examples using the class¶

Mixture of experts

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

Table of Contents

Previous topic

Next topic

This Page

ExpertMixture¶

Examples using the class¶