ó ‡ˆ\c@sÎdZddlmZddlmZddlZddlmZddl m Z ddl m Z m Z d d l mZd d lmZd d lmZd e efd„ƒYZde efd„ƒYZdS(s Various bayesian regression iÿÿÿÿ(tprint_function(tlogN(tlinalg(tpinvhi(t LinearModelt _rescale_datai(tRegressorMixin(t fast_logdet(t check_X_yt BayesianRidgec BsPeZdZddddddeeeeed„ Zdd„Zed„ZRS(s&Bayesian ridge regression Fit a Bayesian ridge model and optimize the regularization parameters lambda (precision of the weights) and alpha (precision of the noise). Read more in the :ref:`User Guide `. Parameters ---------- n_iter : int, optional Maximum number of iterations. Default is 300. tol : float, optional Stop the algorithm if w has converged. Default is 1.e-3. alpha_1 : float, optional Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter. Default is 1.e-6 alpha_2 : float, optional Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter. Default is 1.e-6. lambda_1 : float, optional Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter. Default is 1.e-6. lambda_2 : float, optional Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter. Default is 1.e-6 compute_score : boolean, optional If True, compute the objective function at each step of the model. Default is False fit_intercept : boolean, optional whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered). Default is True. normalize : boolean, optional, default False This parameter is ignored when ``fit_intercept`` is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use :class:`sklearn.preprocessing.StandardScaler` before calling ``fit`` on an estimator with ``normalize=False``. copy_X : boolean, optional, default True If True, X will be copied; else, it may be overwritten. verbose : boolean, optional, default False Verbose mode when fitting the model. Attributes ---------- coef_ : array, shape = (n_features) Coefficients of the regression model (mean of distribution) alpha_ : float estimated precision of the noise. lambda_ : float estimated precision of the weights. sigma_ : array, shape = (n_features, n_features) estimated variance-covariance matrix of the weights scores_ : float if computed, value of the objective function (to be maximized) Examples -------- >>> from sklearn import linear_model >>> clf = linear_model.BayesianRidge() >>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2]) ... # doctest: +NORMALIZE_WHITESPACE BayesianRidge(alpha_1=1e-06, alpha_2=1e-06, compute_score=False, copy_X=True, fit_intercept=True, lambda_1=1e-06, lambda_2=1e-06, n_iter=300, normalize=False, tol=0.001, verbose=False) >>> clf.predict([[1, 1]]) array([1.]) Notes ----- For an example, see :ref:`examples/linear_model/plot_bayesian_ridge.py `. References ---------- D. J. C. MacKay, Bayesian Interpolation, Computation and Neural Systems, Vol. 4, No. 3, 1992. R. Salakhutdinov, Lecture notes on Statistical Machine Learning, http://www.utstat.toronto.edu/~rsalakhu/sta4273/notes/Lecture2.pdf#page=15 Their beta is our ``self.alpha_`` Their alpha is our ``self.lambda_`` i,gü©ñÒMbP?gíµ ÷Æ°>c Csg||_||_||_||_||_||_||_||_| |_| |_ | |_ dS(N( tn_iterttoltalpha_1talpha_2tlambda_1tlambda_2t compute_scoret fit_interceptt normalizetcopy_Xtverbose( tselfR R R R RRRRRRR((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pyt__init__s          c Cs«t||dtjdtƒ\}}|j|||j|j|jd|ƒ\}}}}}|dk r„t |||ƒ\}}n||_ ||_ |j \}}tj tjƒj} dtj|ƒ| } d} |j} |j} |j}|j}|j}tƒ|_d}tj|j|ƒ}tj|dtƒ\}}}|d}xðt|jƒD]ß}||krëtj|j||| | dd…tjfƒ}tj||ƒ}|jrštj tj!| | |ƒƒ }qšn¯tj|jtj||| | ddd…f|jƒƒ}tj||ƒ}|jrštj"|| dtj#| ƒj$ƒ}||c | |7*tj tj!|ƒƒ }n| |_%| |_&tj |tj||ƒdƒ}tj | || | |ƒ}|d| tj |dƒd|} ||d||d|} |jrß| t!| ƒ|| }||t!| ƒ|| 7}|d|t!| ƒ|t!| ƒ| || tj |dƒ||t!dtj'ƒ7}|jj(|ƒn|d kr3tj tj)||ƒƒ|j*kr3| r/t+d t,|ƒd ƒnPntj-|ƒ}qcW||_.tj|j||| | dd…tjfƒ}d| ||_/|j0|||ƒ|S( sFit the model Parameters ---------- X : numpy array of shape [n_samples,n_features] Training data y : numpy array of shape [n_samples] Target values. Will be cast to X's dtype if necessary sample_weight : numpy array of shape [n_samples] Individual weights for each sample .. versionadded:: 0.20 parameter *sample_weight* support to BayesianRidge. Returns ------- self : returns an instance of self. tdtypet y_numerict sample_weightgð?t full_matricesiNgà?isConvergence after s iterations(1Rtnptfloat64tTruet_preprocess_dataRRRtNoneRt X_offset_tX_scale_tshapetfinfotepstvarRRRR R tlisttscores_tdottTRtsvdtFalsetrangeR tnewaxisRtsumRtfulltarrayRtalpha_tlambda_tpitappendtabsR tprinttstrtcopytcoef_tsigma_t_set_intercept(RtXtyRR t y_offset_R!t n_samplest n_featuresR$R1R2RRRR R t coef_old_tXT_ytUtStVht eigen_vals_titer_R9t logdet_sigma_trmse_tgamma_tsR:((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pytfits„$            " !.   #   <1  (cCsŒ|j|ƒ}|tkr|S|jr?||j|j}ntj||jƒ|jddƒ}tj |d|j ƒ}||fSdS(sœPredict using the linear model. In addition to the mean of the predictive distribution, also its standard deviation can be returned. Parameters ---------- X : {array-like, sparse matrix}, shape = (n_samples, n_features) Samples. return_std : boolean, optional Whether to return the standard deviation of posterior prediction. Returns ------- y_mean : array, shape = (n_samples,) Mean of predictive distribution of query points. y_std : array, shape = (n_samples,) Standard deviation of predictive distribution of query points. taxisigð?N( t_decision_functionR+RR R!RR(R:R.tsqrtR1(RR<t return_stdty_meantsigmas_squared_dataty_std((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pytpredicts  %N( t__name__t __module__t__doc__R+RRRRLRT(((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pyR sf    vt ARDRegressionc BsPeZdZddddddedeeeed„ Zd„Zed„ZRS(snBayesian ARD regression. Fit the weights of a regression model, using an ARD prior. The weights of the regression model are assumed to be in Gaussian distributions. Also estimate the parameters lambda (precisions of the distributions of the weights) and alpha (precision of the distribution of the noise). The estimation is done by an iterative procedures (Evidence Maximization) Read more in the :ref:`User Guide `. Parameters ---------- n_iter : int, optional Maximum number of iterations. Default is 300 tol : float, optional Stop the algorithm if w has converged. Default is 1.e-3. alpha_1 : float, optional Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter. Default is 1.e-6. alpha_2 : float, optional Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter. Default is 1.e-6. lambda_1 : float, optional Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter. Default is 1.e-6. lambda_2 : float, optional Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter. Default is 1.e-6. compute_score : boolean, optional If True, compute the objective function at each step of the model. Default is False. threshold_lambda : float, optional threshold for removing (pruning) weights with high precision from the computation. Default is 1.e+4. fit_intercept : boolean, optional whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered). Default is True. normalize : boolean, optional, default False This parameter is ignored when ``fit_intercept`` is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use :class:`sklearn.preprocessing.StandardScaler` before calling ``fit`` on an estimator with ``normalize=False``. copy_X : boolean, optional, default True. If True, X will be copied; else, it may be overwritten. verbose : boolean, optional, default False Verbose mode when fitting the model. Attributes ---------- coef_ : array, shape = (n_features) Coefficients of the regression model (mean of distribution) alpha_ : float estimated precision of the noise. lambda_ : array, shape = (n_features) estimated precisions of the weights. sigma_ : array, shape = (n_features, n_features) estimated variance-covariance matrix of the weights scores_ : float if computed, value of the objective function (to be maximized) Examples -------- >>> from sklearn import linear_model >>> clf = linear_model.ARDRegression() >>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2]) ... # doctest: +NORMALIZE_WHITESPACE ARDRegression(alpha_1=1e-06, alpha_2=1e-06, compute_score=False, copy_X=True, fit_intercept=True, lambda_1=1e-06, lambda_2=1e-06, n_iter=300, normalize=False, threshold_lambda=10000.0, tol=0.001, verbose=False) >>> clf.predict([[1, 1]]) array([1.]) Notes ----- For an example, see :ref:`examples/linear_model/plot_ard.py `. References ---------- D. J. C. MacKay, Bayesian nonlinear modeling for the prediction competition, ASHRAE Transactions, 1994. R. Salakhutdinov, Lecture notes on Statistical Machine Learning, http://www.utstat.toronto.edu/~rsalakhu/sta4273/notes/Lecture2.pdf#page=15 Their beta is our ``self.alpha_`` Their alpha is our ``self.lambda_`` ARD is a little different than the slide: only dimensions/features for which ``self.lambda_ < self.threshold_lambda`` are kept and the rest are discarded. i,gü©ñÒMbP?gíµ ÷Æ°>gˆÃ@c Csp||_||_| |_| |_||_||_||_||_||_||_ | |_ | |_ dS(N( R R RRR R RRRtthreshold_lambdaRR( RR R R R RRRRYRRRR((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pyRšs           c Cs‰t||dtjdtddƒ\}}|j\}}tj|ƒ}|j|||j|j|j ƒ\}}}}}tj |dt ƒ} |j } |j } |j} |j} |j}tjtjƒj}dtj|ƒ|}tj |ƒ}tƒ|_d }d„}d„}xüt|jƒD]ë}||||| |ƒ}|||||| |ƒ}tj|tj||ƒdƒ}d|| tj|ƒ}|d| || dd| || <||jƒd| |d| }||jk} d || <|jr¼| tj|ƒ| |jƒ}|| t|ƒ| |7}|d t|ƒ|t|ƒtjtj|ƒƒ7}|d ||||djƒ8}|jj |ƒn|d krtjtj!||ƒƒ|j"kr|rt#d |ƒnPntj$|ƒ}q,W||||| |ƒ}|||||| |ƒ}||_%||_&||_'||_(|j)|||ƒ|S( s3Fit the ARDRegression model according to the given training data and parameters. Iterative procedure to maximize the evidence Parameters ---------- X : array-like, shape = [n_samples, n_features] Training vector, where n_samples in the number of samples and n_features is the number of features. y : array, shape = [n_samples] Target values (integers). Will be cast to X's dtype if necessary Returns ------- self : returns an instance of self. RRtensure_min_samplesigð?cSs!ttj|ƒ|tj|dd…|ftjd||ddgƒ|dd…|fjƒƒ}tj||dd…|ftjd||ddgƒƒ}tjtjd||ddgƒ|dd…|fj|ƒ }|jdd|jdd…cd||7<|S(Ngð?iiÿÿÿÿ(RRteyeR(treshapeR)tflatR"(R<R1R2t keep_lambdaR?R:((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pyt update_sigmaÚs $#!/cSs=|tj|tj|dd…|fj|ƒƒ||<|S(N(RR(R)(R<R=R9R1R^R:((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pyt update_coeffæs 0g@igà?sConverged after %s iterationsN(*RRRRR"tzerosRRRRtonestboolRRR R RR#R$R%R&R'RR,R R.R(tdiagRYRRRR4R5R R6R8R9R1R:R2R;(RR<R=R?R@R9R R>R!R^RRR R RR$R1R2RAR_R`RGR:RIRJRK((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pyRL«sf-       #    !$1    cCs®|j|ƒ}|tkr|S|jr?||j|j}n|dd…|j|jkf}tj||j ƒ|j ddƒ}tj |d|j ƒ}||fSdS(sœPredict using the linear model. In addition to the mean of the predictive distribution, also its standard deviation can be returned. Parameters ---------- X : {array-like, sparse matrix}, shape = (n_samples, n_features) Samples. return_std : boolean, optional Whether to return the standard deviation of posterior prediction. Returns ------- y_mean : array, shape = (n_samples,) Mean of predictive distribution of query points. y_std : array, shape = (n_samples,) Standard deviation of predictive distribution of query points. NRMigð?( RNR+RR R!R2RYRR(R:R.ROR1(RR<RPRQRRRS((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pyRTs  "%(RURVRWR+RRRLRT(((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pyRX*sn    m(RWt __future__RtmathRtnumpyRtscipyRt scipy.linalgRtbaseRRRt utils.extmathRtutilsRR RX(((s9lib/python2.7/site-packages/sklearn/linear_model/bayes.pyts ÿ