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sklearn
- Sklearn

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type tag = [

| `BayesianGaussianMixture

]

type t =
  [ `BaseEstimator
  | `BaseMixture
  | `BayesianGaussianMixture
  | `DensityMixin
  | `Object ]
    Obj.t

val of_pyobject : Py.Object.t -> t

val to_pyobject : [> tag ] Obj.t -> Py.Object.t

val as_mixture : t -> [ `BaseMixture ] Obj.t

val as_estimator : t -> [ `BaseEstimator ] Obj.t

val as_density : t -> [ `DensityMixin ] Obj.t

val create : 
  ?n_components:int ->
  ?covariance_type:[ `Full | `Tied | `Diag | `Spherical ] ->
  ?tol:float ->
  ?reg_covar:float ->
  ?max_iter:int ->
  ?n_init:int ->
  ?init_params:[ `Kmeans | `Random ] ->
  ?weight_concentration_prior_type:string ->
  ?weight_concentration_prior:float ->
  ?mean_precision_prior:float ->
  ?mean_prior:[> `ArrayLike ] Np.Obj.t ->
  ?degrees_of_freedom_prior:float ->
  ?covariance_prior:[> `ArrayLike ] Np.Obj.t ->
  ?random_state:int ->
  ?warm_start:bool ->
  ?verbose:int ->
  ?verbose_interval:int ->
  unit ->
  t

Variational Bayesian estimation of a Gaussian mixture.

This class allows to infer an approximate posterior distribution over the parameters of a Gaussian mixture distribution. The effective number of components can be inferred from the data.

This class implements two types of prior for the weights distribution: a finite mixture model with Dirichlet distribution and an infinite mixture model with the Dirichlet Process. In practice Dirichlet Process inference algorithm is approximated and uses a truncated distribution with a fixed maximum number of components (called the Stick-breaking representation). The number of components actually used almost always depends on the data.

.. versionadded:: 0.18

Read more in the :ref:`User Guide <bgmm>`.

Parameters ---------- n_components : int, defaults to 1. The number of mixture components. Depending on the data and the value of the `weight_concentration_prior` the model can decide to not use all the components by setting some component `weights_` to values very close to zero. The number of effective components is therefore smaller than n_components.

covariance_type : 'full', 'tied', 'diag', 'spherical', defaults to 'full' String describing the type of covariance parameters to use. Must be one of::

'full' (each component has its own general covariance matrix), 'tied' (all components share the same general covariance matrix), 'diag' (each component has its own diagonal covariance matrix), 'spherical' (each component has its own single variance).

tol : float, defaults to 1e-3. The convergence threshold. EM iterations will stop when the lower bound average gain on the likelihood (of the training data with respect to the model) is below this threshold.

reg_covar : float, defaults to 1e-6. Non-negative regularization added to the diagonal of covariance. Allows to assure that the covariance matrices are all positive.

max_iter : int, defaults to 100. The number of EM iterations to perform.

n_init : int, defaults to 1. The number of initializations to perform. The result with the highest lower bound value on the likelihood is kept.

init_params : 'kmeans', 'random', defaults to 'kmeans'. The method used to initialize the weights, the means and the covariances. Must be one of::

'kmeans' : responsibilities are initialized using kmeans. 'random' : responsibilities are initialized randomly.

weight_concentration_prior_type : str, defaults to 'dirichlet_process'. String describing the type of the weight concentration prior. Must be one of::

'dirichlet_process' (using the Stick-breaking representation), 'dirichlet_distribution' (can favor more uniform weights).

weight_concentration_prior : float | None, optional. The dirichlet concentration of each component on the weight distribution (Dirichlet). This is commonly called gamma in the literature. The higher concentration puts more mass in the center and will lead to more components being active, while a lower concentration parameter will lead to more mass at the edge of the mixture weights simplex. The value of the parameter must be greater than 0. If it is None, it's set to ``1. / n_components``.

mean_precision_prior : float | None, optional. The precision prior on the mean distribution (Gaussian). Controls the extent of where means can be placed. Larger values concentrate the cluster means around `mean_prior`. The value of the parameter must be greater than 0. If it is None, it is set to 1.

mean_prior : array-like, shape (n_features,), optional The prior on the mean distribution (Gaussian). If it is None, it is set to the mean of X.

degrees_of_freedom_prior : float | None, optional. The prior of the number of degrees of freedom on the covariance distributions (Wishart). If it is None, it's set to `n_features`.

covariance_prior : float or array-like, optional The prior on the covariance distribution (Wishart). If it is None, the emiprical covariance prior is initialized using the covariance of X. The shape depends on `covariance_type`::

(n_features, n_features) if 'full', (n_features, n_features) if 'tied', (n_features) if 'diag', float if 'spherical'

random_state : int, RandomState instance or None, optional (default=None) Controls the random seed given to the method chosen to initialize the parameters (see `init_params`). In addition, it controls the generation of random samples from the fitted distribution (see the method `sample`). Pass an int for reproducible output across multiple function calls. See :term:`Glossary <random_state>`.

warm_start : bool, default to False. If 'warm_start' is True, the solution of the last fitting is used as initialization for the next call of fit(). This can speed up convergence when fit is called several times on similar problems. See :term:`the Glossary <warm_start>`.

verbose : int, default to 0. Enable verbose output. If 1 then it prints the current initialization and each iteration step. If greater than 1 then it prints also the log probability and the time needed for each step.

verbose_interval : int, default to 10. Number of iteration done before the next print.

Attributes ---------- weights_ : array-like, shape (n_components,) The weights of each mixture components.

means_ : array-like, shape (n_components, n_features) The mean of each mixture component.

covariances_ : array-like The covariance of each mixture component. The shape depends on `covariance_type`::

(n_components,) if 'spherical', (n_features, n_features) if 'tied', (n_components, n_features) if 'diag', (n_components, n_features, n_features) if 'full'

precisions_ : array-like The precision matrices for each component in the mixture. A precision matrix is the inverse of a covariance matrix. A covariance matrix is symmetric positive definite so the mixture of Gaussian can be equivalently parameterized by the precision matrices. Storing the precision matrices instead of the covariance matrices makes it more efficient to compute the log-likelihood of new samples at test time. The shape depends on ``covariance_type``::

(n_components,) if 'spherical', (n_features, n_features) if 'tied', (n_components, n_features) if 'diag', (n_components, n_features, n_features) if 'full'

precisions_cholesky_ : array-like The cholesky decomposition of the precision matrices of each mixture component. A precision matrix is the inverse of a covariance matrix. A covariance matrix is symmetric positive definite so the mixture of Gaussian can be equivalently parameterized by the precision matrices. Storing the precision matrices instead of the covariance matrices makes it more efficient to compute the log-likelihood of new samples at test time. The shape depends on ``covariance_type``::

(n_components,) if 'spherical', (n_features, n_features) if 'tied', (n_components, n_features) if 'diag', (n_components, n_features, n_features) if 'full'

converged_ : bool True when convergence was reached in fit(), False otherwise.

n_iter_ : int Number of step used by the best fit of inference to reach the convergence.

lower_bound_ : float Lower bound value on the likelihood (of the training data with respect to the model) of the best fit of inference.

weight_concentration_prior_ : tuple or float The dirichlet concentration of each component on the weight distribution (Dirichlet). The type depends on ``weight_concentration_prior_type``::

(float, float) if 'dirichlet_process' (Beta parameters), float if 'dirichlet_distribution' (Dirichlet parameters).

The higher concentration puts more mass in the center and will lead to more components being active, while a lower concentration parameter will lead to more mass at the edge of the simplex.

weight_concentration_ : array-like, shape (n_components,) The dirichlet concentration of each component on the weight distribution (Dirichlet).

mean_precision_prior_ : float The precision prior on the mean distribution (Gaussian). Controls the extent of where means can be placed. Larger values concentrate the cluster means around `mean_prior`. If mean_precision_prior is set to None, `mean_precision_prior_` is set to 1.

mean_precision_ : array-like, shape (n_components,) The precision of each components on the mean distribution (Gaussian).

mean_prior_ : array-like, shape (n_features,) The prior on the mean distribution (Gaussian).

degrees_of_freedom_prior_ : float The prior of the number of degrees of freedom on the covariance distributions (Wishart).

degrees_of_freedom_ : array-like, shape (n_components,) The number of degrees of freedom of each components in the model.

covariance_prior_ : float or array-like The prior on the covariance distribution (Wishart). The shape depends on `covariance_type`::

(n_features, n_features) if 'full', (n_features, n_features) if 'tied', (n_features) if 'diag', float if 'spherical'

See Also -------- GaussianMixture : Finite Gaussian mixture fit with EM.

References ----------

.. 1 `Bishop, Christopher M. (2006). 'Pattern recognition and machine learning'. Vol. 4 No. 4. New York: Springer. <https://www.springer.com/kr/book/9780387310732>`_

.. 2 `Hagai Attias. (2000). 'A Variational Bayesian Framework for Graphical Models'. In Advances in Neural Information Processing Systems 12. <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.2841&rep=rep1&type=pdf>`_

.. 3 `Blei, David M. and Michael I. Jordan. (2006). 'Variational inference for Dirichlet process mixtures'. Bayesian analysis 1.1 <https://www.cs.princeton.edu/courses/archive/fall11/cos597C/reading/BleiJordan2005.pdf>`_

val fit : ?y:Py.Object.t -> x:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> t

Estimate model parameters with the EM algorithm.

The method fits the model ``n_init`` times and sets the parameters with which the model has the largest likelihood or lower bound. Within each trial, the method iterates between E-step and M-step for ``max_iter`` times until the change of likelihood or lower bound is less than ``tol``, otherwise, a ``ConvergenceWarning`` is raised. If ``warm_start`` is ``True``, then ``n_init`` is ignored and a single initialization is performed upon the first call. Upon consecutive calls, training starts where it left off.

Parameters ---------- X : array-like, shape (n_samples, n_features) List of n_features-dimensional data points. Each row corresponds to a single data point.

Returns ------- self

val fit_predict : 
  ?y:Py.Object.t ->
  x:[> `ArrayLike ] Np.Obj.t ->
  [> tag ] Obj.t ->
  [> `ArrayLike ] Np.Obj.t

Estimate model parameters using X and predict the labels for X.

The method fits the model n_init times and sets the parameters with which the model has the largest likelihood or lower bound. Within each trial, the method iterates between E-step and M-step for `max_iter` times until the change of likelihood or lower bound is less than `tol`, otherwise, a :class:`~sklearn.exceptions.ConvergenceWarning` is raised. After fitting, it predicts the most probable label for the input data points.

.. versionadded:: 0.20

Parameters ---------- X : array-like, shape (n_samples, n_features) List of n_features-dimensional data points. Each row corresponds to a single data point.

Returns ------- labels : array, shape (n_samples,) Component labels.

val get_params : ?deep:bool -> [> tag ] Obj.t -> Dict.t

Get parameters for this estimator.

Parameters ---------- deep : bool, default=True If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns ------- params : mapping of string to any Parameter names mapped to their values.

val predict : 
  x:[> `ArrayLike ] Np.Obj.t ->
  [> tag ] Obj.t ->
  [> `ArrayLike ] Np.Obj.t

Predict the labels for the data samples in X using trained model.

Parameters ---------- X : array-like, shape (n_samples, n_features) List of n_features-dimensional data points. Each row corresponds to a single data point.

Returns ------- labels : array, shape (n_samples,) Component labels.

val predict_proba : 
  x:[> `ArrayLike ] Np.Obj.t ->
  [> tag ] Obj.t ->
  [> `ArrayLike ] Np.Obj.t

Predict posterior probability of each component given the data.

Parameters ---------- X : array-like, shape (n_samples, n_features) List of n_features-dimensional data points. Each row corresponds to a single data point.

Returns ------- resp : array, shape (n_samples, n_components) Returns the probability each Gaussian (state) in the model given each sample.

val sample : 
  ?n_samples:int ->
  [> tag ] Obj.t ->
  [> `ArrayLike ] Np.Obj.t * [> `ArrayLike ] Np.Obj.t

Generate random samples from the fitted Gaussian distribution.

Parameters ---------- n_samples : int, optional Number of samples to generate. Defaults to 1.

Returns ------- X : array, shape (n_samples, n_features) Randomly generated sample

y : array, shape (nsamples,) Component labels

val score : 
  ?y:Py.Object.t ->
  x:[> `ArrayLike ] Np.Obj.t ->
  [> tag ] Obj.t ->
  float

Compute the per-sample average log-likelihood of the given data X.

Parameters ---------- X : array-like, shape (n_samples, n_dimensions) List of n_features-dimensional data points. Each row corresponds to a single data point.

Returns ------- log_likelihood : float Log likelihood of the Gaussian mixture given X.

val score_samples : 
  x:[> `ArrayLike ] Np.Obj.t ->
  [> tag ] Obj.t ->
  [> `ArrayLike ] Np.Obj.t

Compute the weighted log probabilities for each sample.

Parameters ---------- X : array-like, shape (n_samples, n_features) List of n_features-dimensional data points. Each row corresponds to a single data point.

Returns ------- log_prob : array, shape (n_samples,) Log probabilities of each data point in X.

val set_params : ?params:(string * Py.Object.t) list -> [> tag ] Obj.t -> t

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form ``<component>__<parameter>`` so that it's possible to update each component of a nested object.

Parameters ---------- **params : dict Estimator parameters.

Returns ------- self : object Estimator instance.

val weights_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute weights_: get value or raise Not_found if None.

val weights_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute weights_: get value as an option.

val means_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute means_: get value or raise Not_found if None.

val means_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute means_: get value as an option.

val covariances_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute covariances_: get value or raise Not_found if None.

val covariances_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute covariances_: get value as an option.

val precisions_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute precisions_: get value or raise Not_found if None.

val precisions_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute precisions_: get value as an option.

val precisions_cholesky_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute precisions_cholesky_: get value or raise Not_found if None.

val precisions_cholesky_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute precisions_cholesky_: get value as an option.

val converged_ : t -> bool

Attribute converged_: get value or raise Not_found if None.

val converged_opt : t -> bool option

Attribute converged_: get value as an option.

val n_iter_ : t -> int

Attribute n_iter_: get value or raise Not_found if None.

val n_iter_opt : t -> int option

Attribute n_iter_: get value as an option.

val lower_bound_ : t -> float

Attribute lower_bound_: get value or raise Not_found if None.

val lower_bound_opt : t -> float option

Attribute lower_bound_: get value as an option.

val weight_concentration_prior_ : t -> Py.Object.t

Attribute weight_concentration_prior_: get value or raise Not_found if None.

val weight_concentration_prior_opt : t -> Py.Object.t option

Attribute weight_concentration_prior_: get value as an option.

val weight_concentration_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute weight_concentration_: get value or raise Not_found if None.

val weight_concentration_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute weight_concentration_: get value as an option.

val mean_precision_prior_ : t -> float

Attribute mean_precision_prior_: get value or raise Not_found if None.

val mean_precision_prior_opt : t -> float option

Attribute mean_precision_prior_: get value as an option.

val mean_precision_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute mean_precision_: get value or raise Not_found if None.

val mean_precision_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute mean_precision_: get value as an option.

val mean_prior_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute mean_prior_: get value or raise Not_found if None.

val mean_prior_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute mean_prior_: get value as an option.

val degrees_of_freedom_prior_ : t -> float

Attribute degrees_of_freedom_prior_: get value or raise Not_found if None.

val degrees_of_freedom_prior_opt : t -> float option

Attribute degrees_of_freedom_prior_: get value as an option.

val degrees_of_freedom_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute degrees_of_freedom_: get value or raise Not_found if None.

val degrees_of_freedom_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute degrees_of_freedom_: get value as an option.

val covariance_prior_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute covariance_prior_: get value or raise Not_found if None.

val covariance_prior_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute covariance_prior_: get value as an option.

val to_string : t -> string

Print the object to a human-readable representation.

val show : t -> string

Print the object to a human-readable representation.

val pp : Format.formatter -> t -> unit

Pretty-print the object to a formatter.