MixtureFactory¶

class otmixmod.MixtureFactory(*args)¶

Mixture inference.

Parameters:

atomsNumberint: The number of atoms
covarianceModelstr, optional: The covariance model. Default is ‘Gaussian_pk_Lk_C’ See GetValidCovarianceModels() for available models

Methods

`BuildClusters`(data, labels, nbClusters)	Partition a given sample into nbClusters according to the given labels.
`GetValidCovarianceModels`()	Available covariance models names accessor.
`build`(*args)	Build the distribution.
`buildAsMixture`(sample)	Mixture inference.
`buildEstimator`(*args)	Build the distribution and the parameter distribution.
`getAtomsNumber`()	Atoms number accessor.
`getBootstrapSize`()	Accessor to the bootstrap size.
`getClassName`()	Accessor to the object's name.
`getKnownParameterIndices`()	Accessor to the known parameters indices.
`getKnownParameterValues`()	Accessor to the known parameters values.
`getName`()	Accessor to the object's name.
`hasName`()	Test if the object is named.
`setAtomsNumber`(number)	Atoms number accessor.
`setBootstrapSize`(bootstrapSize)	Accessor to the bootstrap size.
`setKnownParameter`(values, positions)	Accessor to the known parameters.
`setName`(name)	Accessor to the object's name.
`setSeed`(seed)	Mixmod RNG seed accessor.

getCovarianceModel
setCovarianceModel

Notes

Each value of the covarianceModel parameter defines a specific parametrization of the mixture of Gaussians. See (Biernacki et al., 2006) table 1 page 290 for details on these different parametrizations.

References

Biernacki C., Celeux G., Govaert G., Langrognet F., (2006). Model-Based Cluster and Discriminant Analysis with the MIXMOD Software. Computational Statistics and Data Analysis, vol. 51/2, pp. 587-600.

Examples

Estimate the parameters of the mixture of 2 Gaussians.

>>> import openturns as ot
>>> import otmixmod

>>> factory = otmixmod.MixtureFactory(2, 'Gaussian_pk_L_Dk_A_Dk')
>>> sample = [
...     [1.5, 0.7],
...     [0.2, -0.6],
...     [2.1, 0.1],
...     [1.2, 2.4],
...     [2.2, 0.0],
...     [-0.9, -2.1],
...     [-1.7, -0.3],
...     [0.7, 0.4],
...     [-1.2, 1.1],
...     [-0.5, -1.1],
... ]
>>> estimatedDistribution, labels, logLikelihood = factory.build(sample)

__init__(*args)¶

static BuildClusters(data, labels, nbClusters)¶

Partition a given sample into nbClusters according to the given labels.

Parameters:

data2-d sequence of float: The sample
labelssequence of int: The index of the class of each point in the sample
nbClustersint: The number of clusters in the mixture

Returns:

clusterssequence of openturns.Sample: The list of samples corresponding to each class

static GetValidCovarianceModels()¶

Available covariance models names accessor.

Returns:

namesopenturns.Description: Valid covariance model names

Examples

>>> import otmixmod
>>> otmixmod.MixtureFactory.GetValidCovarianceModels()[:3]
[Gaussian_p_L_I,Gaussian_p_Lk_I,Gaussian_p_L_B]

build(*args)¶

Build the distribution.

Available usages:

build()

build(sample)

build(param)

Parameters:

sample2-d sequence of float: Data.
paramsequence of float: The parameters of the distribution.

Returns:

distDistribution

The estimated distribution.

In the first usage, the default native distribution is built.

buildAsMixture(sample)¶

Mixture inference.

Parameters:

sampleopenturns.Sample: Sample

Returns:

mixtureopenturns.Mixture: Inferred distribution

buildEstimator(*args)¶

Build the distribution and the parameter distribution.

Parameters:

sample2-d sequence of float: Data.
parametersDistributionParameters: Optional, the parametrization.

Returns:

resDistDistributionFactoryResult: The results.

Notes

According to the way the native parameters of the distribution are estimated, the parameters distribution differs:

Moments method: the asymptotic parameters distribution is normal and estimated by Bootstrap on the initial data;

Maximum likelihood method with a regular model: the asymptotic parameters distribution is normal and its covariance matrix is the inverse Fisher information matrix;

Other methods: the asymptotic parameters distribution is estimated by Bootstrap on the initial data and kernel fitting (see KernelSmoothing).

If another set of parameters is specified, the native parameters distribution is first estimated and the new distribution is determined from it:

if the native parameters distribution is normal and the transformation regular at the estimated parameters values: the asymptotic parameters distribution is normal and its covariance matrix determined from the inverse Fisher information matrix of the native parameters and the transformation;

in the other cases, the asymptotic parameters distribution is estimated by Bootstrap on the initial data and kernel fitting.

getAtomsNumber()¶

Atoms number accessor.

Returns:

atomsNumberint: The number of atoms

getBootstrapSize()¶

Accessor to the bootstrap size.

Returns:

sizeint: Size of the bootstrap.

getClassName()¶

Accessor to the object’s name.

Returns:

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

getKnownParameterIndices()¶

Accessor to the known parameters indices.

Returns:

indicesIndices: Indices of the known parameters.

getKnownParameterValues()¶

Accessor to the known parameters values.

Returns:

valuesPoint: Values of known parameters.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

setAtomsNumber(number)¶

Atoms number accessor.

Parameters:

atomsNumberint: The number of atoms

setBootstrapSize(bootstrapSize)¶

Accessor to the bootstrap size.

Parameters:

sizeint: The size of the bootstrap.

setKnownParameter(values, positions)¶

Accessor to the known parameters.

Parameters:

valuessequence of float: Values of known parameters.
positionssequence of int: Indices of known parameters.

Examples

When a subset of the parameter vector is known, the other parameters only have to be estimated from data.

In the following example, we consider a sample and want to fit a Beta distribution. We assume that the $a$ and $b$ parameters are known beforehand. In this case, we set the third parameter (at index 2) to -1 and the fourth parameter (at index 3) to 1.

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Beta(2.3, 2.2, -1.0, 1.0)
>>> sample = distribution.getSample(10)
>>> factory = ot.BetaFactory()
>>> # set (a,b) out of (r, t, a, b)
>>> factory.setKnownParameter([-1.0, 1.0], [2, 3])
>>> inf_distribution = factory.build(sample)

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setSeed(seed)¶

Mixmod RNG seed accessor.

Parameters:

seedint: Seed used to initialize the Mixmod RNG seed before the learning step. A negative seed will randomly initialize the RNG. The default value is 0.

MixtureFactory¶

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