ó ‡ˆ\c@ sàdZddlmZddlZddlZddlmZmZddl m Z ddl m Z d d „Z d efd „ƒYZed d„Zed d„Zdefd„ƒYZed„Zdefd„ƒYZdS(s² Covariance estimators using shrinkage. Shrinkage corresponds to regularising `cov` using a convex combination: shrunk_cov = (1-shrinkage)*cov + shrinkage*structured_estimate. iÿÿÿÿ(tdivisionNi(tempirical_covariancetEmpiricalCovariancei(txrange(t check_arraygš™™™™™¹?cC sbt|ƒ}|jd}tj|ƒ|}d||}|jdd|d…c||7<|S(s’Calculates a covariance matrix shrunk on the diagonal Read more in the :ref:`User Guide `. 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 igð?Ni(Rtshapetnpttracetflat(temp_covt shrinkaget n_featurestmut shrunk_cov((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pytshrunk_covariances   $tShrunkCovariancecB s,eZdZeedd„Zdd„ZRS(sËCovariance estimator with shrinkage Read more in the :ref:`User Guide `. Parameters ---------- store_precision : boolean, default True Specify if the estimated precision is stored assume_centered : boolean, default False If True, data are not centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False, data are centered before computation. shrinkage : float, 0 <= shrinkage <= 1, default 0.1 Coefficient in the convex combination used for the computation of the shrunk estimate. Attributes ---------- location_ : array-like, shape (n_features,) Estimated location, i.e. the estimated mean. covariance_ : array-like, shape (n_features, n_features) Estimated covariance matrix precision_ : array-like, shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) shrinkage : float, 0 <= shrinkage <= 1 Coefficient in the convex combination used for the computation of the shrunk estimate. 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]]) >>> np.random.seed(0) >>> X = np.random.multivariate_normal(mean=[0, 0], ... cov=real_cov, ... size=500) >>> cov = ShrunkCovariance().fit(X) >>> cov.covariance_ # doctest: +ELLIPSIS array([[0.7387..., 0.2536...], [0.2536..., 0.4110...]]) >>> cov.location_ array([0.0622..., 0.0193...]) Notes ----- The regularized covariance is given by: (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features) where mu = trace(cov) / n_features gš™™™™™¹?cC s,tt|ƒjd|d|ƒ||_dS(Ntstore_precisiontassume_centered(tsuperRt__init__R (tselfRRR ((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pyR€scC s{t|ƒ}|jr1tj|jdƒ|_n|jdƒ|_t|d|jƒ}t||j ƒ}|j |ƒ|S(s¾ Fits the shrunk covariance model according to the given training data and parameters. Parameters ---------- X : array-like, shape = [n_samples, n_features] Training data, where n_samples is the number of samples and n_features is the number of features. y not used, present for API consistence purpose. Returns ------- self : object iiR( RRRtzerosRt location_tmeanRRR t_set_covariance(RtXtyt covariance((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pytfit†s   N(t__name__t __module__t__doc__tTruetFalseRtNoneR(((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pyRAs> ièc C s-tj|ƒ}t|jƒdkr;|jddkr;dS|jdkr_tj|d ƒ}n|jddkr‚tjdƒn|j\}}|s­||jdƒ}nt ||ƒ}|d}tj |ddƒ|}tj |ƒ|}d} d} xpt |ƒD]b} xºt |ƒD]¬} t || || dƒ} t || || dƒ}| tj tj |j| |dd…|fƒƒ7} | tj tj |j| |dd…|fƒdƒ7} qWt || || dƒ} | tj tj |j| |dd…||d…fƒƒ7} | tj tj |j| |dd…||d…fƒdƒ7} q Wx§t |ƒD]™} t || || dƒ}| tj tj |j|||dd…|fƒƒ7} | tj tj |j|||dd…|fƒdƒ7} qW| tj tj |j|||dd…||d…fƒdƒ7} | |d} | tj tj |j|||dd…||d…fƒƒ7} d ||| || }| d ||j ƒ||d}||}t||ƒ}|dkrdn||}|S( s¸Estimates the shrunk Ledoit-Wolf covariance matrix. Read more in the :ref:`User Guide `. 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 are not centered before computation. Useful to work with data whose mean is significantly equal to zero but is not exactly zero. If False, data are 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 iigiÿÿÿÿisBOnly one sample available. You may want to reshape your data arraytaxisNgð?g@(iiÿÿÿÿ(RtasarraytlenRtndimtreshapetwarningstwarnRtinttsumRtslicetdottTtmin(RRt block_sizet n_samplesR tn_splitstX2t emp_cov_traceR tbeta_tdelta_titjtrowstcolstbetatdeltaR ((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pytledoit_wolf_shrinkage©sT"( 6>@ ?: 9+'$ c C s>tj|ƒ}t|jƒdkrm|jddkrm|sP||jƒ}ntj|djƒƒdfS|jdkr­tj|d ƒ}tj dƒd}|j }n|j\}}t |d|d|ƒ}t |d|ƒ}tj tj|ƒƒ|}d||}|jd d |d…c||7<||fS( seEstimates the shrunk Ledoit-Wolf covariance matrix. Read more in the :ref:`User Guide `. 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 are not centered before computation. Useful to work with data whose mean is significantly equal to zero but is not exactly zero. If False, data are 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 iigiÿÿÿÿsBOnly one sample available. You may want to reshape your data arrayRR0gð?N(iiÿÿÿÿ(RR$R%RRt atleast_2dR&R'R(R)tsizeR=RR+RR( RRR0R1R R R R R ((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pyt ledoit_wolfs$&(  $t LedoitWolfcB s,eZdZeedd„Zdd„ZRS(s/ 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 are not centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False (default), data are centered before computation. block_size : int, default=1000 Size of the 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 ---------- location_ : array-like, shape (n_features,) Estimated location, i.e. the estimated mean. covariance_ : array-like, shape (n_features, n_features) Estimated covariance matrix precision_ : array-like, shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) shrinkage_ : float, 0 <= shrinkage <= 1 Coefficient in the convex combination used for the computation of the shrunk estimate. 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_ # doctest: +ELLIPSIS array([[0.4406..., 0.1616...], [0.1616..., 0.8022...]]) >>> cov.location_ array([ 0.0595... , -0.0075...]) 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. iècC s,tt|ƒjd|d|ƒ||_dS(NRR(RRARR0(RRRR0((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pyR”scC s…t|ƒ}|jr1tj|jdƒ|_n|jdƒ|_t||jdtd|j ƒ\}}||_ |j |ƒ|S(sÉ Fits the Ledoit-Wolf shrunk covariance model according to the given training data and parameters. Parameters ---------- X : array-like, shape = [n_samples, n_features] Training data, where n_samples is the number of samples and n_features is the number of features. y not used, present for API consistence purpose. Returns ------- self : object iiRR0( RRRRRRRR@R R0t shrinkage_R(RRRRR ((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pyRšs    N(RRRR R!RR"R(((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pyRAHsK c C s}tj|ƒ}t|jƒdkrm|jddkrm|sP||jƒ}ntj|djƒƒdfS|jdkr­tj|d ƒ}tj dƒd}|j }n|j\}}t |d|ƒ}tj |ƒ|}tj|dƒ}||d}|d||d|}|dkr.dnt ||dƒ} d| |} | jd d |d…c| |7<| | fS( sEstimate 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 are not centered before computation. Useful to work with data whose mean is significantly equal to zero but is not exactly zero. If False, data are 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. iigiÿÿÿÿsBOnly one sample available. You may want to reshape your data arrayRgð?iN(iiÿÿÿÿ(RR$R%RRR>R&R'R(R)R?RRR/R( RRR1R R R talphatnumtdenR R ((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pytoas½s(#(  %$tOAScB seZdZdd„ZRS(sEOracle 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 are not centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False (default), data are centered before computation. Attributes ---------- covariance_ : array-like, shape (n_features, n_features) Estimated covariance matrix. precision_ : array-like, shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) shrinkage_ : float, 0 <= shrinkage <= 1 coefficient in the convex combination used for the computation of the shrunk estimate. 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. cC s|t|ƒ}|jr1tj|jdƒ|_n|jdƒ|_t||jdtƒ\}}||_ |j |ƒ|S(sÕ Fits the Oracle Approximating Shrinkage covariance model according to the given training data and parameters. Parameters ---------- X : array-like, shape = [n_samples, n_features] Training data, where n_samples is the number of samples and n_features is the number of features. y not used, present for API consistence purpose. Returns ------- self : object iiR( RRRRRRRRFR RBR(RRRRR ((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pyR5s    N(RRRR"R(((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pyRGþs5(Rt __future__RR(tnumpyRtempirical_covariance_RRtexternals.six.movesRtutilsRRRR!R=R@RARFRG(((sDlib/python2.7/site-packages/sklearn/covariance/shrunk_covariance_.pyts    &h_@u A