package sklearn

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package sklearn

sklearn
- Sklearn

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module EllipticEnvelope : sig ... end

module EmpiricalCovariance : sig ... end

module GraphicalLasso : sig ... end

module GraphicalLassoCV : sig ... end

module LedoitWolf : sig ... end

module MinCovDet : sig ... end

module OAS : sig ... end

module ShrunkCovariance : sig ... end

val empirical_covariance : 
  ?assume_centered:bool ->
  x:Ndarray.t ->
  unit ->
  Py.Object.t

Computes the Maximum likelihood covariance estimator

Parameters ---------- X : ndarray, shape (n_samples, n_features) Data from which to compute the covariance estimate

assume_centered : boolean If True, data will not be centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False, data will be centered before computation.

Returns ------- covariance : 2D ndarray, shape (n_features, n_features) Empirical covariance (Maximum Likelihood Estimator).

val fast_mcd : 
  ?support_fraction:[ `Float of float | `PyObject of Py.Object.t ] ->
  ?cov_computation_method:Py.Object.t ->
  ?random_state:[ `Int of int | `RandomState of Py.Object.t | `None ] ->
  x:Ndarray.t ->
  unit ->
  Ndarray.t * Ndarray.t * Py.Object.t

Estimates the Minimum Covariance Determinant matrix.

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

Parameters ---------- X : array-like, shape (n_samples, n_features) The data matrix, with p features and n samples.

support_fraction : float, 0 < support_fraction < 1 The proportion of points to be included in the support of the raw MCD estimate. Default is None, which implies that the minimum value of support_fraction will be used within the algorithm: `n_sample + n_features + 1 / 2`.

cov_computation_method : callable, default empirical_covariance The function which will be used to compute the covariance. Must return shape (n_features, n_features)

random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`.

Notes ----- The FastMCD algorithm has been introduced by Rousseuw and Van Driessen in "A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS". The principle is to compute robust estimates and random subsets before pooling them into a larger subsets, and finally into the full data set. Depending on the size of the initial sample, we have one, two or three such computation levels.

Note that only raw estimates are returned. If one is interested in the correction and reweighting steps described in RouseeuwVan_, see the MinCovDet object.

References ----------

.. RouseeuwVan A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS

.. Butler1993 R. W. Butler, P. L. Davies and M. Jhun, Asymptotics For The Minimum Covariance Determinant Estimator, The Annals of Statistics, 1993, Vol. 21, No. 3, 1385-1400

Returns ------- location : array-like, shape (n_features,) Robust location of the data.

covariance : array-like, shape (n_features, n_features) Robust covariance of the features.

support : array-like, type boolean, shape (n_samples,) A mask of the observations that have been used to compute the robust location and covariance estimates of the data set.

val graphical_lasso : 
  ?cov_init:Py.Object.t ->
  ?mode:[ `Cd | `Lars ] ->
  ?tol:float ->
  ?enet_tol:float ->
  ?max_iter:int ->
  ?verbose:bool ->
  ?return_costs:bool ->
  ?eps:float ->
  ?return_n_iter:bool ->
  emp_cov:Py.Object.t ->
  alpha:float ->
  unit ->
  Py.Object.t * Py.Object.t * Py.Object.t * int

l1-penalized covariance estimator

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

Parameters ---------- emp_cov : 2D ndarray, shape (n_features, n_features) Empirical covariance from which to compute the covariance estimate.

alpha : positive float The regularization parameter: the higher alpha, the more regularization, the sparser the inverse covariance.

cov_init : 2D array (n_features, n_features), optional The initial guess for the covariance.

mode : 'cd', 'lars' The Lasso solver to use: coordinate descent or LARS. Use LARS for very sparse underlying graphs, where p > n. Elsewhere prefer cd which is more numerically stable.

tol : positive float, optional The tolerance to declare convergence: if the dual gap goes below this value, iterations are stopped.

enet_tol : positive float, optional The tolerance for the elastic net solver used to calculate the descent direction. This parameter controls the accuracy of the search direction for a given column update, not of the overall parameter estimate. Only used for mode='cd'.

max_iter : integer, optional The maximum number of iterations.

verbose : boolean, optional If verbose is True, the objective function and dual gap are printed at each iteration.

return_costs : boolean, optional If return_costs is True, the objective function and dual gap at each iteration are returned.

eps : float, optional The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems.

return_n_iter : bool, optional Whether or not to return the number of iterations.

Returns ------- covariance : 2D ndarray, shape (n_features, n_features) The estimated covariance matrix.

precision : 2D ndarray, shape (n_features, n_features) The estimated (sparse) precision matrix.

costs : list of (objective, dual_gap) pairs The list of values of the objective function and the dual gap at each iteration. Returned only if return_costs is True.

n_iter : int Number of iterations. Returned only if `return_n_iter` is set to True.

See Also -------- GraphicalLasso, GraphicalLassoCV

Notes ----- The algorithm employed to solve this problem is the GLasso algorithm, from the Friedman 2008 Biostatistics paper. It is the same algorithm as in the R `glasso` package.

One possible difference with the `glasso` R package is that the diagonal coefficients are not penalized.

val ledoit_wolf : 
  ?assume_centered:bool ->
  ?block_size:int ->
  x:Ndarray.t ->
  unit ->
  Ndarray.t * float

Estimates the shrunk Ledoit-Wolf covariance matrix.

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

Parameters ---------- X : array-like, shape (n_samples, n_features) Data from which to compute the covariance estimate

assume_centered : boolean, default=False If True, data will not be centered before computation. Useful to work with data whose mean is significantly equal to zero but is not exactly zero. If False, data will be centered before computation.

block_size : int, default=1000 Size of the blocks into which the covariance matrix will be split. This is purely a memory optimization and does not affect results.

Returns ------- shrunk_cov : array-like, shape (n_features, n_features) Shrunk covariance.

shrinkage : float Coefficient in the convex combination used for the computation of the shrunk estimate.

Notes ----- The regularized (shrunk) covariance is:

(1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)

where mu = trace(cov) / n_features

val ledoit_wolf_shrinkage : 
  ?assume_centered:bool ->
  ?block_size:int ->
  x:Ndarray.t ->
  unit ->
  float

Estimates the shrunk Ledoit-Wolf covariance matrix.

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

Parameters ---------- X : array-like, shape (n_samples, n_features) Data from which to compute the Ledoit-Wolf shrunk covariance shrinkage.

assume_centered : bool If True, data will not be centered before computation. Useful to work with data whose mean is significantly equal to zero but is not exactly zero. If False, data will be centered before computation.

block_size : int Size of the blocks into which the covariance matrix will be split.

Returns ------- shrinkage : float Coefficient in the convex combination used for the computation of the shrunk estimate.

Notes ----- The regularized (shrunk) covariance is:

(1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)

where mu = trace(cov) / n_features

val log_likelihood : 
  emp_cov:Py.Object.t ->
  precision:Py.Object.t ->
  unit ->
  Py.Object.t

Computes the sample mean of the log_likelihood under a covariance model

computes the empirical expected log-likelihood (accounting for the normalization terms and scaling), allowing for universal comparison (beyond this software package)

Parameters ---------- emp_cov : 2D ndarray (n_features, n_features) Maximum Likelihood Estimator of covariance

precision : 2D ndarray (n_features, n_features) The precision matrix of the covariance model to be tested

Returns ------- sample mean of the log-likelihood

val oas : ?assume_centered:bool -> x:Ndarray.t -> unit -> Ndarray.t * float

Estimate covariance with the Oracle Approximating Shrinkage algorithm.

Parameters ---------- X : array-like, shape (n_samples, n_features) Data from which to compute the covariance estimate.

assume_centered : boolean If True, data will not be centered before computation. Useful to work with data whose mean is significantly equal to zero but is not exactly zero. If False, data will be centered before computation.

Returns ------- shrunk_cov : array-like, shape (n_features, n_features) Shrunk covariance.

shrinkage : float Coefficient in the convex combination used for the computation of the shrunk estimate.

Notes ----- The regularised (shrunk) covariance is:

(1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)

where mu = trace(cov) / n_features

The formula we used to implement the OAS is slightly modified compared to the one given in the article. See :class:`OAS` for more details.

val shrunk_covariance : 
  ?shrinkage:[ `Float of float | `PyObject of Py.Object.t ] ->
  emp_cov:Ndarray.t ->
  unit ->
  Ndarray.t

Calculates a covariance matrix shrunk on the diagonal

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

Parameters ---------- emp_cov : array-like, shape (n_features, n_features) Covariance matrix to be shrunk

shrinkage : float, 0 <= shrinkage <= 1 Coefficient in the convex combination used for the computation of the shrunk estimate.

Returns ------- shrunk_cov : array-like Shrunk covariance.

Notes ----- The regularized (shrunk) covariance is given by:

(1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)

where mu = trace(cov) / n_features