-iXqSrSSKJr SSKJrJr SSKrSSKJ r SSK J r SSK J r Jr SS KJr SS KJr SS KJr SS KJrJr S SKJrJrJr "SS\ \5r"SS\ \5rg)z Various bayesian regression )log)IntegralRealN)linalg)pinvh)RegressorMixin _fit_context)_safe_indexing)Interval) fast_logdet)_check_sample_weight validate_data) LinearModel_preprocess_data _rescale_datac$\rSrSr%Sr\"\SSSS9/\"\SSSS9/\"\SSSS9/\"\SSSS9/\"\SSSS9/\"\SSSS9/S\"\SSSS9/S\"\SSSS9/S /S /S /S /S . r\ \ S 'S SSSSSSSSSSSS . Sjr \ "SS9SSj5r SSjrSrSrSrg) BayesianRidgea\Bayesian ridge regression. Fit a Bayesian ridge model. See the Notes section for details on this implementation and the optimization of the regularization parameters lambda (precision of the weights) and alpha (precision of the noise). Read more in the :ref:`User Guide `. For an intuitive visualization of how the sinusoid is approximated by a polynomial using different pairs of initial values, see :ref:`sphx_glr_auto_examples_linear_model_plot_bayesian_ridge_curvefit.py`. Parameters ---------- max_iter : int, default=300 Maximum number of iterations over the complete dataset before stopping independently of any early stopping criterion. .. versionchanged:: 1.3 tol : float, default=1e-3 Stop the algorithm if w has converged. alpha_1 : float, default=1e-6 Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter. alpha_2 : float, default=1e-6 Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter. lambda_1 : float, default=1e-6 Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter. lambda_2 : float, default=1e-6 Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter. alpha_init : float, default=None Initial value for alpha (precision of the noise). If not set, alpha_init is 1/Var(y). .. versionadded:: 0.22 lambda_init : float, default=None Initial value for lambda (precision of the weights). If not set, lambda_init is 1. .. versionadded:: 0.22 compute_score : bool, default=False If True, compute the log marginal likelihood at each iteration of the optimization. fit_intercept : bool, default=True Whether to calculate the intercept for this model. The intercept is not treated as a probabilistic parameter and thus has no associated variance. If set to False, no intercept will be used in calculations (i.e. data is expected to be centered). copy_X : bool, default=True If True, X will be copied; else, it may be overwritten. verbose : bool, default=False Verbose mode when fitting the model. Attributes ---------- coef_ : array-like of shape (n_features,) Coefficients of the regression model (mean of distribution) intercept_ : float Independent term in decision function. Set to 0.0 if `fit_intercept = False`. alpha_ : float Estimated precision of the noise. lambda_ : float Estimated precision of the weights. sigma_ : array-like of shape (n_features, n_features) Estimated variance-covariance matrix of the weights scores_ : array-like of shape (n_iter_+1,) If computed_score is True, value of the log marginal likelihood (to be maximized) at each iteration of the optimization. The array starts with the value of the log marginal likelihood obtained for the initial values of alpha and lambda and ends with the value obtained for the estimated alpha and lambda. n_iter_ : int The actual number of iterations to reach the stopping criterion. X_offset_ : ndarray of shape (n_features,) If `fit_intercept=True`, offset subtracted for centering data to a zero mean. Set to np.zeros(n_features) otherwise. X_scale_ : ndarray of shape (n_features,) Set to np.ones(n_features). 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 -------- ARDRegression : Bayesian ARD regression. Notes ----- There exist several strategies to perform Bayesian ridge regression. This implementation is based on the algorithm described in Appendix A of (Tipping, 2001) where updates of the regularization parameters are done as suggested in (MacKay, 1992). Note that according to A New View of Automatic Relevance Determination (Wipf and Nagarajan, 2008) these update rules do not guarantee that the marginal likelihood is increasing between two consecutive iterations of the optimization. References ---------- D. J. C. MacKay, Bayesian Interpolation, Computation and Neural Systems, Vol. 4, No. 3, 1992. M. E. Tipping, Sparse Bayesian Learning and the Relevance Vector Machine, Journal of Machine Learning Research, Vol. 1, 2001. Examples -------- >>> from sklearn import linear_model >>> clf = linear_model.BayesianRidge() >>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2]) BayesianRidge() >>> clf.predict([[1, 1]]) array([1.]) rNleftclosedrneitherbooleanverbose max_itertolalpha_1alpha_2lambda_1lambda_2 alpha_init lambda_init compute_score fit_interceptcopy_Xr_parameter_constraints,MbP?ư>FTc XlX lX0lX@lXPlX`lXplXlXlXl Xl Xl gNr) selfrrr r!r"r#r$r%r&r'r(rs N/var/www/html/venv/lib/python3.13/site-packages/sklearn/linear_model/_bayes.py__init__BayesianRidge.__init__sC !     $&**  prefer_skip_nested_validationc [UUU[R[R/SSS9upURnUR upVUnUR 5nUbH[X1US9nUR5n[R"X#S9n [R"X)- S-US9n[UUURURUS9uppn Ub[XU5upn XlXl[R "[R5R"nUR$nUR&nUcSX-- nUcSn[R("XS9n[R("UUS9nUR*nUR,nUR.nUR0nUR2n[55UlSn[R8"UR:U5n[<R>"XU:S 9unnn[AU5nUS-n[RB"XdS9nUUS U&US U2SS24n[EURF5GH7nURIXXVUUUUUU5 un n!URJ(a3URMUUUUUUU U!5n"UR6ROU"5 [R"UU-UUU--- 5n#U#SU--[R"U S-5SU--- nUU#- SU--U!SU--- nUS :waZ[R"[RP"UU - 55URR:aU(a[US [WU5S 5 O[RX"U 5nGM: WS -Ul-Xl.UUl/URIXXVUUUUUU5 uUl0n!URJ(aXURMUUUUUUW U!5n"UR6ROU"5 [Rb"UR65Ul[R8"UR:UUU-U-SS2[Rd4- 5Ul3URiXU 5 U$)aFit the model. Parameters ---------- X : ndarray of shape (n_samples, n_features) Training data. y : ndarray of shape (n_samples,) Target values. Will be cast to X's dtype if necessary. sample_weight : ndarray of shape (n_samples,), default=None Individual weights for each sample. .. versionadded:: 0.20 parameter *sample_weight* support to BayesianRidge. Returns ------- self : object Returns the instance itself. T)dtypeforce_writeable y_numericNr7)weightsr)r'copy sample_weight?) full_matricesrzConvergence after z iterationsr)5rnpfloat64float32r7shapevarrsumaveragerr'r(r X_offset_X_scale_finfoepsr$r%asarrayrr"r#r r!listscores_dotTrsvdlenzerosranger _update_coef_r&_log_marginal_likelihoodappendabsrprintstrr<n_iter_alpha_lambda_coef_arraynewaxissigma__set_intercept)$r/Xyr=r7 n_samples n_featuressw_sumy_vary_meanrG y_offset_rH_rJr[r\rr"r#r r! coef_old_XT_yUSVh_fullK eigen_vals_eigen_vals_fullVhiter_r]sse_sgamma_s$ r0fitBayesianRidge.fits",  ::rzz*    !   $0OM"&&(FZZ9FJJ q0-HE/? ,,' 0 ,iH  $#A-8GA!" hhrzz"&&"" >EK(F ?GF0**WE2,,====,,,,v  vvacc1~ 15KM 1g Fd ((:;*! QqS!V_4==)E,,iT1b+vwKE4!!11  ##A&VVVk1g@T6TUVFH ,q1AAL1PQGvoG 3q7{8JKFzbffRVVI,=%>?$((J.E MJI=*@qy   -- )q"k67  D   -- A LL   "88DLL1DLff IIw&?":W"Dam!TT   I(; r3cURU5nU(dU$[R"XR5U-R SS9n[R "USUR - -5nX54$)0Predict 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} of shape (n_samples, n_features) Samples. return_std : bool, default=False Whether to return the standard deviation of posterior prediction. Returns ------- y_mean : array-like of shape (n_samples,) Mean of predictive distribution of query points. y_std : array-like of shape (n_samples,) Standard deviation of predictive distribution of query points. raxisr>)_decision_functionr@rNr`rEsqrtr[)r/rb return_stdrhsigmas_squared_datay_stds r0predictBayesianRidge.predictxsg,((+M#%66![[#9A#="B"B"B"J GG/33DEFE= r3c X4:aI[RRURXxX- -SS2[R4- U/5n OE[RRURXhX- -SSS24- URU/5n [R "U[R "X5- S-5n X4$)zUpdate posterior mean and compute corresponding sse (sum of squared errors). Posterior mean is given by coef_ = scaled_sigma_ * X.T * y where scaled_sigma_ = (lambda_/alpha_ * np.eye(n_features) + np.dot(X.T, X))^-1 Nr)r@r multi_dotrOr_rErN) r/rbrcrdrerlrmrsrqr[r\r]rus r0rTBayesianRidge._update_coef_s  !II''r7+;;Q ]KKTREII''a)9947CCQSS!LE vvq266!++12{r3c URn URn URn URn X:a1[R "[R "XeU--55*n On[R"X&[R"U5RS9n U SU===XT-- sss&[R "[R "U 55*n U [ U5-X-- nX[ U5-X-- - nUSU[ U5-U[ U5--XX-- U[R "US-5-- U -U[ S[R-5-- -- nU$)zLog marginal likelihood.r:N?r) r r!r"r#r@rErfullr^r7pi)r/rdrerf eigen_valsr[r\coefsser r!r"r# logdet_sigmascores r0rU&BayesianRidge._log_marginal_likelihoodsN,,,,====  !FF266'Z4G*G#HIIL77:bhhw>O>U>UVL ) $(; ; $FF266,#788L3w<'(*<< 3v;&)999  W %s6{" #l tQw' (   s1ruu9~%  &   r3)rGrHr[r r!r$r]r&r(r'r\r"r#r%rrZrMr`rrr.F)__name__ __module__ __qualname____firstlineno____doc__r rrr)dict__annotations__r1r rxrrTrU__static_attributes__r3r0rrsOdh4?@q$y9:T1d6:;T1d6:;dAtF;<dAtF;<XdAtFCDhtQVDE##+; $D $ :5]6]~!<2r3rc\rSrSr%Sr\"\SSSS9/\"\SSSS9/\"\SSSS9/\"\SSSS9/\"\SSSS9/\"\SSSS9/S/\"\SSSS9/S/S/S /S . r\ \ S 'S S SSSSSSSSSS . Sjr \ "SS9S5r SrSrSSjrSrg) ARDRegressioniaBayesian 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 ---------- max_iter : int, default=300 Maximum number of iterations. .. versionchanged:: 1.3 tol : float, default=1e-3 Stop the algorithm if w has converged. alpha_1 : float, default=1e-6 Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter. alpha_2 : float, default=1e-6 Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter. lambda_1 : float, default=1e-6 Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter. lambda_2 : float, default=1e-6 Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter. compute_score : bool, default=False If True, compute the objective function at each step of the model. threshold_lambda : float, default=10 000 Threshold for removing (pruning) weights with high precision from the computation. fit_intercept : bool, default=True Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered). copy_X : bool, default=True If True, X will be copied; else, it may be overwritten. verbose : bool, default=False Verbose mode when fitting the model. Attributes ---------- coef_ : array-like of shape (n_features,) Coefficients of the regression model (mean of distribution) alpha_ : float estimated precision of the noise. lambda_ : array-like of shape (n_features,) estimated precisions of the weights. sigma_ : array-like of shape (n_features, n_features) estimated variance-covariance matrix of the weights scores_ : float if computed, value of the objective function (to be maximized) n_iter_ : int The actual number of iterations to reach the stopping criterion. .. versionadded:: 1.3 intercept_ : float Independent term in decision function. Set to 0.0 if ``fit_intercept = False``. X_offset_ : float If `fit_intercept=True`, offset subtracted for centering data to a zero mean. Set to np.zeros(n_features) otherwise. X_scale_ : float Set to np.ones(n_features). 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 -------- BayesianRidge : Bayesian ridge regression. 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. Examples -------- >>> from sklearn import linear_model >>> clf = linear_model.ARDRegression() >>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2]) ARDRegression() >>> clf.predict([[1, 1]]) array([1.]) - :ref:`sphx_glr_auto_examples_linear_model_plot_ard.py` demonstrates ARD Regression. - :ref:`sphx_glr_auto_examples_linear_model_plot_lasso_and_elasticnet.py` showcases ARD Regression alongside Lasso and Elastic-Net for sparse, correlated signals, in the presence of noise. rNrrrrr) rrr r!r"r#r&threshold_lambdar'r(rr)r*r+r,Fg@Tc XlX lXlX0lX@lXPlX`lXplXlXl Xl gr.) rrr'r r!r"r#r&rr(r) r/rrr r!r"r#r&rr'r(rs r0r1ARDRegression.__init__fs>! *    * 0  r3r4c [UUU[R[R/SSSS9upURnUR upE[R "XSS9n[XURURS9uppxn Xpl Xl [R"U[S9n URn URn UR n UR"nUR$n[R&"[R5R(n[R*"S[R,"U5U-- US9n[R"XSS9n[/5UlSnSnXE:a UR2O UR4n[7UR85GHnU"UUUU 5nU"XUUU U5n[R:"U[R<"X5- S-5nSUU [R>"U5-- nUS U --XjS-S U --- UU 'UUR;5- S U --US U--- nUUR@:n S Xj)'URB(aU [RD"U5-U U-- R;5nUU [EU5-UU-- - nUS [GU5U[EU5--[R:"[RD"U55--- nUS UU-UUS--R;5---nUR0RIU5 US :aR[R:"[RJ"UU- 55URL:aU(a[OS U-5 O2[RP"U5nU RS5(aGM O WS -Ul*U RS5(aU"UUUU 5nU"XUUU U5nO&[RV"/5RYS S 5nX`l-UUl.UUl/UUl0URcXxU 5 U$)aFit the model according to the given training data and parameters. Iterative procedure to maximize the evidence Parameters ---------- X : array-like of shape (n_samples, n_features) Training vector, where `n_samples` is the number of samples and `n_features` is the number of features. y : array-like of shape (n_samples,) Target values (integers). Will be cast to X's dtype if necessary. Returns ------- self : object Fitted estimator. 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