U 3d[@sdZddlZddlmZmZddlZddlmZm Z ddl m Z ddl m Z dd lmZdd d ZGd dde ZdddZdddddZGddde ZddddZGddde ZdS)z Covariance estimators using shrinkage. Shrinkage corresponds to regularising `cov` using a convex combination: shrunk_cov = (1-shrinkage)*cov + shrinkage*structured_estimate. N)RealIntegral)empirical_covarianceEmpiricalCovariance)config_context) check_array)Interval皙?cCsPt|}|jd}t||}d||}|jdd|d||7<|S)aCalculate a covariance matrix shrunk on the diagonal. Read more in the :ref:`User Guide `. Parameters ---------- emp_cov : array-like of shape (n_features, n_features) Covariance matrix to be shrunk. shrinkage : float, default=0.1 Coefficient in the convex combination used for the computation of the shrunk estimate. Range is [0, 1]. Returns ------- shrunk_cov : ndarray of shape (n_features, n_features) 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`. r?Nr)r shapenptraceflat)emp_cov shrinkage n_featuresmu shrunk_covrI/tmp/pip-unpacked-wheel-zrfo1fqw/sklearn/covariance/_shrunk_covariance.pyshrunk_covariances    rcsZeZdZUdZejdeeddddgiZee d<dd d d fd d Z dddZ Z S)ShrunkCovariancea Covariance estimator with shrinkage. Read more in the :ref:`User Guide `. Parameters ---------- store_precision : bool, default=True Specify if the estimated precision is stored. assume_centered : bool, default=False 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. shrinkage : float, default=0.1 Coefficient in the convex combination used for the computation of the shrunk estimate. Range is [0, 1]. Attributes ---------- covariance_ : ndarray of shape (n_features, n_features) Estimated covariance matrix location_ : ndarray of shape (n_features,) Estimated location, i.e. the estimated mean. precision_ : ndarray of shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- EllipticEnvelope : An object for detecting outliers in a Gaussian distributed dataset. EmpiricalCovariance : Maximum likelihood covariance estimator. GraphicalLasso : Sparse inverse covariance estimation with an l1-penalized estimator. GraphicalLassoCV : Sparse inverse covariance with cross-validated choice of the l1 penalty. LedoitWolf : LedoitWolf Estimator. MinCovDet : Minimum Covariance Determinant (robust estimator of covariance). OAS : Oracle Approximating Shrinkage Estimator. Notes ----- The regularized covariance is given by: (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features) where mu = trace(cov) / n_features Examples -------- >>> import numpy as np >>> from sklearn.covariance import ShrunkCovariance >>> from sklearn.datasets import make_gaussian_quantiles >>> real_cov = np.array([[.8, .3], ... [.3, .4]]) >>> rng = np.random.RandomState(0) >>> X = rng.multivariate_normal(mean=[0, 0], ... cov=real_cov, ... size=500) >>> cov = ShrunkCovariance().fit(X) >>> cov.covariance_ array([[0.7387..., 0.2536...], [0.2536..., 0.4110...]]) >>> cov.location_ array([0.0622..., 0.0193...]) rrrZbothclosed_parameter_constraintsTFr )store_precisionassume_centeredrcstj||d||_dSN)rr)super__init__r)selfrrr __class__rrr!s zShrunkCovariance.__init__NcCs`|||}|jr,t|jd|_n |d|_t||jd}t ||j }| ||S)aFit the shrunk covariance model to X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where `n_samples` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Returns the instance itself. rrr) _validate_params_validate_datarrzerosr location_meanrrr_set_covariance)r"Xy covariancerrrfits    zShrunkCovariance.fit)N) __name__ __module__ __qualname____doc__rrr rdict__annotations__r!r/ __classcell__rrr#rrBs TrFc Cs4t|}t|jdkr(|jddkr(dS|jdkr>t|d}|jddkrVtd|j\}}|sr||d}t ||}|d}tj |dd|}t ||}d} d} t |D] } t |D]} t || || d} t || || d}| t t |j| |dd|f7} | t t |j| |dd|fd7} qt || || d} | t t |j| |dd||df7} | t t |j| |dd||dfd7} qt |D]} t || || d}| t t |j||d|dd|f7} | t t |j||d|dd|fd7} q| t t |j||d|dd||dfd7} | |d} | t t |j||d|dd||df7} d ||| || }| d || ||d}||}t||}|dkr(dn||}|S) aEstimate the shrunk Ledoit-Wolf covariance matrix. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like of shape (n_samples, n_features) Data from which to compute the Ledoit-Wolf shrunk covariance shrinkage. assume_centered : bool, 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 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 rrrrBOnly one sample available. You may want to reshape your data array)ZaxisNr g@)r lenr ndimrreshapewarningswarnr*intsumrangeslicedotTmin)r,r block_size n_samplesrZn_splitsZX2Z emp_cov_tracerZbeta_Zdelta_ijZrowscolsbetadeltarrrrledoit_wolf_shrinkagesX!     (.06 080 ,  rOrrHc Cst|}t|jdkrJ|jddkrJ|s4||}t|ddfS|jdkrrt|d}t d|j }n |j\}}t |||d}t ||d}t t||}d||}|jd d |d||7<||fS) afEstimate the shrunk Ledoit-Wolf covariance matrix. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like of shape (n_samples, n_features) Data from which to compute the covariance estimate. assume_centered : bool, 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 blocks into which the covariance matrix will be split. This is purely a memory optimization and does not affect results. Returns ------- shrunk_cov : ndarray of 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 rrr8r9r;rPr%r N)r r<r r*r atleast_2dr=r>r?r@sizerOrrBrr) r,rrHr_rrrrrrr ledoit_wolf#s,%       rTcsZeZdZUdZejdeeddddgiZee d<dd d d fd d Z dddZ Z S) LedoitWolfa LedoitWolf Estimator. Ledoit-Wolf is a particular form of shrinkage, where the shrinkage coefficient is computed using O. Ledoit and M. Wolf's formula as described in "A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices", Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2, February 2004, pages 365-411. Read more in the :ref:`User Guide `. Parameters ---------- store_precision : bool, default=True Specify if the estimated precision is stored. assume_centered : bool, default=False If True, data will not be centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False (default), data will be centered before computation. block_size : int, default=1000 Size of blocks into which the covariance matrix will be split during its Ledoit-Wolf estimation. This is purely a memory optimization and does not affect results. Attributes ---------- covariance_ : ndarray of shape (n_features, n_features) Estimated covariance matrix. location_ : ndarray of shape (n_features,) Estimated location, i.e. the estimated mean. precision_ : ndarray of shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) shrinkage_ : float Coefficient in the convex combination used for the computation of the shrunk estimate. Range is [0, 1]. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- EllipticEnvelope : An object for detecting outliers in a Gaussian distributed dataset. EmpiricalCovariance : Maximum likelihood covariance estimator. GraphicalLasso : Sparse inverse covariance estimation with an l1-penalized estimator. GraphicalLassoCV : Sparse inverse covariance with cross-validated choice of the l1 penalty. MinCovDet : Minimum Covariance Determinant (robust estimator of covariance). OAS : Oracle Approximating Shrinkage Estimator. ShrunkCovariance : Covariance estimator with shrinkage. Notes ----- The regularised covariance is: (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features) where mu = trace(cov) / n_features and shrinkage is given by the Ledoit and Wolf formula (see References) References ---------- "A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices", Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2, February 2004, pages 365-411. Examples -------- >>> import numpy as np >>> from sklearn.covariance import LedoitWolf >>> real_cov = np.array([[.4, .2], ... [.2, .8]]) >>> np.random.seed(0) >>> X = np.random.multivariate_normal(mean=[0, 0], ... cov=real_cov, ... size=50) >>> cov = LedoitWolf().fit(X) >>> cov.covariance_ array([[0.4406..., 0.1616...], [0.1616..., 0.8022...]]) >>> cov.location_ array([ 0.0595... , -0.0075...]) rHrNleftrrTFr7)rrrHcstj||d||_dSr)r r!rH)r"rrrHr#rrr!s zLedoitWolf.__init__c Cs||||}|jr,t|jd|_n |d|_tdd t ||jd|j d\}}W5QRX||_ | ||S)aFit the Ledoit-Wolf shrunk covariance model to X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where `n_samples` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Returns the instance itself. rrT)Z assume_finiterP) r&r'rrr(r r)r*rrTrH shrinkage_r+r"r,r-r.rrrrr/s    zLedoitWolf.fit)N) r0r1r2r3rrr rr4r5r!r/r6rrr#rrUcs erUr%c Cst|}t|jdkrL|jddkrL|s6||}t|ddfS|jdkrxt|d}t dd}|j }n |j\}}t ||d}t ||}t|d}||d}|d||d|}|dkrdn t ||d} d| |} | jd d |d| |7<| | fS) aEstimate covariance with the Oracle Approximating Shrinkage algorithm. Parameters ---------- X : array-like of shape (n_samples, n_features) Data from which to compute the covariance estimate. assume_centered : bool, 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. Returns ------- shrunk_cov : array-like of 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. rrr8r9r;r%r rN)rZasarrayr<r r*rQr=r>r?r@rRrrrGr) r,rrIrrralphanumZdenrrrrroass,"         r[c@seZdZdZdddZdS)OASa Oracle Approximating Shrinkage Estimator. Read more in the :ref:`User Guide `. OAS is a particular form of shrinkage described in "Shrinkage Algorithms for MMSE Covariance Estimation" Chen et al., IEEE Trans. on Sign. Proc., Volume 58, Issue 10, October 2010. The formula used here does not correspond to the one given in the article. In the original article, formula (23) states that 2/p is multiplied by Trace(cov*cov) in both the numerator and denominator, but this operation is omitted because for a large p, the value of 2/p is so small that it doesn't affect the value of the estimator. Parameters ---------- store_precision : bool, default=True Specify if the estimated precision is stored. assume_centered : bool, default=False If True, data will not be centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False (default), data will be centered before computation. Attributes ---------- covariance_ : ndarray of shape (n_features, n_features) Estimated covariance matrix. location_ : ndarray of shape (n_features,) Estimated location, i.e. the estimated mean. precision_ : ndarray of shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) shrinkage_ : float coefficient in the convex combination used for the computation of the shrunk estimate. Range is [0, 1]. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- EllipticEnvelope : An object for detecting outliers in a Gaussian distributed dataset. EmpiricalCovariance : Maximum likelihood covariance estimator. GraphicalLasso : Sparse inverse covariance estimation with an l1-penalized estimator. GraphicalLassoCV : Sparse inverse covariance with cross-validated choice of the l1 penalty. LedoitWolf : LedoitWolf Estimator. MinCovDet : Minimum Covariance Determinant (robust estimator of covariance). ShrunkCovariance : Covariance estimator with shrinkage. Notes ----- The regularised covariance is: (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features) where mu = trace(cov) / n_features and shrinkage is given by the OAS formula (see References) References ---------- "Shrinkage Algorithms for MMSE Covariance Estimation" Chen et al., IEEE Trans. on Sign. Proc., Volume 58, Issue 10, October 2010. Examples -------- >>> import numpy as np >>> from sklearn.covariance import OAS >>> from sklearn.datasets import make_gaussian_quantiles >>> real_cov = np.array([[.8, .3], ... [.3, .4]]) >>> rng = np.random.RandomState(0) >>> X = rng.multivariate_normal(mean=[0, 0], ... cov=real_cov, ... size=500) >>> oas = OAS().fit(X) >>> oas.covariance_ array([[0.7533..., 0.2763...], [0.2763..., 0.3964...]]) >>> oas.precision_ array([[ 1.7833..., -1.2431... ], [-1.2431..., 3.3889...]]) >>> oas.shrinkage_ 0.0195... NcCsb|||}|jr,t|jd|_n |d|_t||jdd\}}||_ | ||S)aFit the Oracle Approximating Shrinkage covariance model to X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where `n_samples` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Returns the instance itself. rrTr%) r&r'rrr(r r)r*r[rWr+rXrrrr/s   zOAS.fit)N)r0r1r2r3r/rrrrr\7sfr\)r )Fr7)r3r?ZnumbersrrZnumpyrrr_configrutilsr Zutils._param_validationr rrrOrTrUr[r\rrrrs     % _@A