chaospy.GaussianMixture

class chaospy.GaussianMixture(means, covariances, weights=None, rotation=None)

Gaussian Mixture Model.

A Gaussian mixture model is a probabilistic model that assumes all the data points are generated from a mixture of a finite number of Gaussian distributions with unknown parameters. One can think of mixture models as generalizing K-means clustering to incorporate information about the covariance structure of the data as well as the centers of the latent Gaussians.

Attributes:

means:

Sequence of means.

covariances:

Sequence of covariance matrices.

weights:

How much each sample is weighted. Either a scalar when the samples are equally weighted, or a vector with the same length as the number of mixed models.

Examples:

>>> means = ([0, 1], [1, 0])
>>> covariances = ([[1, 0], [0, 1]], [[1, 0.5], [0.5, 1]])
>>> distribution = GaussianMixture(means, covariances)
>>> uloc = [[0, 0, 1, 1], [0, 1, 0, 1]]
>>> distribution.pdf(uloc).round(4)
array([0.0954, 0.092 , 0.1212, 0.0954])
>>> distribution.fwd(uloc).round(4)
array([[0.3293, 0.3293, 0.6707, 0.6707],
       [0.3699, 0.6731, 0.3711, 0.734 ]])
>>> distribution.inv(uloc).round(4)
array([[-8.9681, -8.9681,  8.0521,  8.0521],
       [-9.862 , 10.1977, -9.5929, 10.2982]])
>>> distribution.mom([(0, 1, 1), (1, 0, 1)]).round(4)
array([0.5 , 0.5 , 0.25])

__init__(means, covariances, weights=None, rotation=None)

Args:

means (numpy.ndarray):

Sequence of mean values. With shape (n_components, n_dim).

covariances (numpy.ndarray):

Sequence of covariance matrices. With shape (n_components, n_dim, n_dim).

weights (Optional[numpy.ndarray]):

Weights of the samples. This must have the shape (n_components,). If omitted, each sample is assumed to be equally weighted.

Methods

pdf(x_data[, decompose, allow_approx, step_size])	Probability density function.
cdf(x_data)	Cumulative distribution function.
fwd(x_data)	Forward Rosenblatt transformation.
inv(q_data[, max_iterations, tollerance])	Inverse Rosenblatt transformation.
sample([size, rule, antithetic, ...])	Create pseudo-random generated samples.
mom(K[, allow_approx])	Raw statistical moments.
ttr(kloc)	Three terms relation's coefficient generator.

Attributes

interpret_as_integer	Flag indicating that return value from the methods sample, and inv should be interpreted as integers instead of floating point.
lower	Lower bound for the distribution.
stochastic_dependent	True if distribution contains stochastically dependent components.
upper	Upper bound for the distribution.