B \@sfdZddlZddlmZmZddlmZddlm Z ddl m Z m Z ddl mZGd d d eeZdS) zFModule :mod:`sklearn.kernel_ridge` implements kernel ridge regression.N) BaseEstimatorRegressorMixin)pairwise_kernels)_solve_cholesky_kernel) check_array check_X_y)check_is_fittedc@sBeZdZdZdddZddd Zed d Zdd d ZddZ dS) 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, array-like}, shape = [n_targets] Small positive values of alpha improve the conditioning of the problem and reduce the variance of the estimates. Alpha corresponds to ``(2*C)^-1`` in other linear models such as LogisticRegression or LinearSVC. If an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number. kernel : string or callable, default="linear" Kernel mapping used internally. A callable should accept two arguments and the keyword arguments passed to this object as kernel_params, and should return a floating point number. Set to "precomputed" in order to pass a precomputed kernel matrix to the estimator methods instead of samples. 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 : mapping of string to any, optional Additional parameters (keyword arguments) for kernel function passed as callable object. Attributes ---------- dual_coef_ : array, shape = [n_samples] or [n_samples, n_targets] Representation of weight vector(s) in kernel space X_fit_ : {array-like, sparse matrix}, shape = [n_samples, n_features] Training data, which is also required for prediction. If kernel == "precomputed" this is instead the precomputed training matrix, shape = [n_samples, n_samples]. References ---------- * Kevin P. Murphy "Machine Learning: A Probabilistic Perspective", The MIT Press chapter 14.4.3, pp. 492-493 See also -------- sklearn.linear_model.Ridge: Linear ridge regression. sklearn.svm.SVR: Support Vector Regression implemented using libsvm. 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) >>> clf = KernelRidge(alpha=1.0) >>> clf.fit(X, y) # doctest: +NORMALIZE_WHITESPACE KernelRidge(alpha=1.0, coef0=1, degree=3, gamma=None, kernel='linear', kernel_params=None) rlinearNcCs(||_||_||_||_||_||_dS)N)alphakernelgammadegreecoef0 kernel_params)selfr rrrrrr3lib/python3.7/site-packages/sklearn/kernel_ridge.py__init__ls zKernelRidge.__init__cCsBt|jr|jpi}n|j|j|jd}t||f|jdd|S)N)rrrT)ZmetricZ filter_params)callablerrrrrr)rXYZparamsrrr _get_kernelus    zKernelRidge._get_kernelcCs |jdkS)N precomputed)r)rrrr _pairwiseszKernelRidge._pairwisecCst||dddd\}}|dk r4t|ts4t|dd}||}t|j}d}t|j dkrl| dd}d}|j d k}t ||||||_ |r|j |_ ||_|S) apFit Kernel Ridge regression model Parameters ---------- X : {array-like, sparse matrix}, shape = [n_samples, n_features] Training data. If kernel == "precomputed" this is instead a precomputed kernel matrix, shape = [n_samples, n_samples]. y : array-like, shape = [n_samples] or [n_samples, n_targets] Target values sample_weight : float or array-like of shape [n_samples] Individual weights for each sample, ignored if None is passed. Returns ------- self : returns an instance of self. )ZcsrZcscT)Z accept_sparseZ multi_outputZ y_numericNF)Z ensure_2drr)r isinstancefloatrrnpZ atleast_1dr lenshapeZreshaperr dual_coef_ravelX_fit_)rryZ sample_weightKr r$copyrrrfits$        zKernelRidge.fitcCs*t|ddg|||j}t||jS)a%Predict using the kernel ridge model Parameters ---------- X : {array-like, sparse matrix}, 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 : array, shape = [n_samples] or [n_samples, n_targets] Returns predicted values. r%r#)r rr%r dotr#)rrr'rrrpredictszKernelRidge.predict)rr Nr rN)N)NN) __name__ __module__ __qualname____doc__rrpropertyrr)r+rrrrr s[   -r )r/Znumpyr baserrZmetrics.pairwiserZlinear_model.ridgerZutilsrrZutils.validationr r rrrrs