-i#SrSSKJr SSKrSSKJrJrJrJ r SSK J r SSK J r Jr SSKJrJr SS KJrJrJr "S S \\\5rg) zKernel ridge regression.)RealN) BaseEstimatorMultiOutputMixinRegressorMixin _fit_context)_solve_cholesky_kernel)PAIRWISE_KERNEL_FUNCTIONSpairwise_kernels)Interval StrOptions)_check_sample_weightcheck_is_fitted validate_datac ^\rSrSr%Sr\"\SSSS9S/\"\"\ R"55S1-5\ /\"\SSSS9S/\"\SSSS9/\"\SSS S9/\ S/S .r \ \S 'SS SSS SS.SjjrSSjrU4Sjr\"SS9SSj5rSrSrU=r$) KernelRidgeaKernel ridge regression. Kernel ridge regression (KRR) combines ridge regression (linear least squares with l2-norm regularization) with the kernel trick. It thus learns a linear function in the space induced by the respective kernel and the data. For non-linear kernels, this corresponds to a non-linear function in the original space. The form of the model learned by KRR is identical to support vector regression (SVR). However, different loss functions are used: KRR uses squared error loss while support vector regression uses epsilon-insensitive loss, both combined with l2 regularization. In contrast to SVR, fitting a KRR model can be done in closed-form and is typically faster for medium-sized datasets. On the other hand, the learned model is non-sparse and thus slower than SVR, which learns a sparse model for epsilon > 0, at prediction-time. This estimator has built-in support for multi-variate regression (i.e., when y is a 2d-array of shape [n_samples, n_targets]). Read more in the :ref:`User Guide `. Parameters ---------- alpha : float or array-like of shape (n_targets,), default=1.0 Regularization strength; must be a positive float. Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to ``1 / (2C)`` in other linear models such as :class:`~sklearn.linear_model.LogisticRegression` or :class:`~sklearn.svm.LinearSVC`. If an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number. See :ref:`ridge_regression` for formula. kernel : str or callable, default="linear" Kernel mapping used internally. This parameter is directly passed to :class:`~sklearn.metrics.pairwise.pairwise_kernels`. If `kernel` is a string, it must be one of the metrics in `pairwise.PAIRWISE_KERNEL_FUNCTIONS` or "precomputed". If `kernel` is "precomputed", X is assumed to be a kernel matrix. Alternatively, if `kernel` is a callable function, it is called on each pair of instances (rows) and the resulting value recorded. The callable should take two rows from X as input and return the corresponding kernel value as a single number. This means that callables from :mod:`sklearn.metrics.pairwise` are not allowed, as they operate on matrices, not single samples. Use the string identifying the kernel instead. gamma : float, default=None Gamma parameter for the RBF, laplacian, polynomial, exponential chi2 and sigmoid kernels. Interpretation of the default value is left to the kernel; see the documentation for sklearn.metrics.pairwise. Ignored by other kernels. degree : float, default=3 Degree of the polynomial kernel. Ignored by other kernels. coef0 : float, default=1 Zero coefficient for polynomial and sigmoid kernels. Ignored by other kernels. kernel_params : dict, default=None Additional parameters (keyword arguments) for kernel function passed as callable object. Attributes ---------- dual_coef_ : ndarray of shape (n_samples,) or (n_samples, n_targets) Representation of weight vector(s) in kernel space X_fit_ : {ndarray, sparse matrix} of shape (n_samples, n_features) Training data, which is also required for prediction. If kernel == "precomputed" this is instead the precomputed training matrix, of shape (n_samples, n_samples). 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 -------- sklearn.gaussian_process.GaussianProcessRegressor : Gaussian Process regressor providing automatic kernel hyperparameters tuning and predictions uncertainty. sklearn.linear_model.Ridge : Linear ridge regression. sklearn.linear_model.RidgeCV : Ridge regression with built-in cross-validation. sklearn.svm.SVR : Support Vector Regression accepting a large variety of kernels. References ---------- * Kevin P. Murphy "Machine Learning: A Probabilistic Perspective", The MIT Press chapter 14.4.3, pp. 492-493 Examples -------- >>> from sklearn.kernel_ridge import KernelRidge >>> import numpy as np >>> n_samples, n_features = 10, 5 >>> rng = np.random.RandomState(0) >>> y = rng.randn(n_samples) >>> X = rng.randn(n_samples, n_features) >>> krr = KernelRidge(alpha=1.0) >>> krr.fit(X, y) KernelRidge(alpha=1.0) rNleft)closedz array-like precomputedneitheralphakernelgammadegreecoef0 kernel_params_parameter_constraintsrlinear)rrrrrcLXlX lX0lX@lXPlX`lgNr)selfrrrrrrs G/var/www/html/venv/lib/python3.13/site-packages/sklearn/kernel_ridge.py__init__KernelRidge.__init__s#     *c[UR5(aUR=(d 0nO$URURUR S.n[ X4URSS.UD6$)N)rrrT)metric filter_params)callablerrrrrr )r$XYparamss r% _get_kernelKernelRidge._get_kernelsU DKK ''-2F#zzT[[4::VFWT[[WPVWWr(c>[TU]5nSURlURS:HURlU$)NTr)super__sklearn_tags__ input_tagssparserpairwise)r$tags __class__s r%r4KernelRidge.__sklearn_tags__s6w')!%#';;-#?  r(T)prefer_skip_nested_validationc [XUSSSS9upUb [U[5(d [X15nUR U5n[ R "UR5nSn[UR5S:XaURSS5nSnURS:Hn[XBXSU5Ul U(aURR5Ul XlU$)aFit Kernel Ridge regression model. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. If kernel == "precomputed" this is instead a precomputed kernel matrix, of shape (n_samples, n_samples). y : array-like of shape (n_samples,) or (n_samples, n_targets) Target values. sample_weight : float or array-like of shape (n_samples,), default=None Individual weights for each sample, ignored if None is passed. Returns ------- self : object Returns the instance itself. csrcscT) accept_sparse multi_output y_numericFrr)r isinstancefloatrr0np atleast_1drlenshapereshaperr dual_coef_ravelX_fit_)r$r-y sample_weightKrrLcopys r%fitKernelRidge.fits, Qn4SW   $Z u-M-M0BM   Q  djj) qww<1  "a AE{{m+0uTR "oo335DO  r(c[U5 [XSSS9nURXR5n[R "X R 5$)aPredict using the kernel ridge model. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) Samples. If kernel == "precomputed" this is instead a precomputed kernel matrix, shape = [n_samples, n_samples_fitted], where n_samples_fitted is the number of samples used in the fitting for this estimator. Returns ------- C : ndarray of shape (n_samples,) or (n_samples, n_targets) Returns predicted values. r=F)r@reset)rrr0rMrFdotrK)r$r-rPs r%predictKernelRidge.predictsA  $u M   Q ,vva))r()rMrrrrKrrr)rr#)__name__ __module__ __qualname____firstlineno____doc__r rr setr keysr,dictr__annotations__r&r0r4rrRrW__static_attributes__ __classcell__)r9s@r%rrsrj4D8,G s499;< N O  4D8$?D!T&9:4tI>? $D ++"X 5*6*X**r(r)r]numbersrnumpyrFbaserrrrlinear_model._ridger metrics.pairwiser r utils._param_validationr r utils.validationrrrrr(r%rls8 OO7I9RR_*"NM_*r(