ó ‡ˆ\c@s‹dZddlZddlmZmZddlmZddlm Z ddl m Z m Z ddl mZd eefd „ƒYZdS( sFModule :mod:`sklearn.kernel_ridge` implements kernel ridge regression.i˙˙˙˙Ni(t BaseEstimatortRegressorMixin(tpairwise_kernels(t_solve_cholesky_kernel(t check_arrayt check_X_y(tcheck_is_fittedt KernelRidgecBs\eZdZddd ddd d„Zd d„Zed„ƒZd d d„Zd„Z RS( söKernel 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) itlinearicCs:||_||_||_||_||_||_dS(N(talphatkerneltgammatdegreetcoef0t kernel_params(tselfR R R R R R((s3lib/python2.7/site-packages/sklearn/kernel_ridge.pyt__init__ls      cCsdt|jƒr!|jpi}n$i|jd6|jd6|jd6}t||d|jdt|S(NR R R tmetrict filter_params(tcallableR RR R R RtTrue(RtXtYtparams((s3lib/python2.7/site-packages/sklearn/kernel_ridge.pyt _get_kernelus   cCs |jdkS(Nt precomputed(R (R((s3lib/python2.7/site-packages/sklearn/kernel_ridge.pyt _pairwisesc Cst||dd dtdtƒ\}}|d k rXt|tƒ rXt|dtƒ}n|j|ƒ}tj |j ƒ}t}t |j ƒdkrŻ|j ddƒ}t}n|jd k}t|||||ƒ|_|rô|jjƒ|_n||_|S( spFit Kernel Ridge regression model Parameters ---------- X : {array-like, sparse matrix}, shape = [n_samples, n_features] Training data. If kernel == "precomputed" this is instead a precomputed kernel matrix, shape = [n_samples, n_samples]. y : array-like, shape = [n_samples] or [n_samples, n_targets] Target values sample_weight : float or array-like of shape [n_samples] Individual weights for each sample, ignored if None is passed. Returns ------- self : returns an instance of self. t accept_sparsetcsrtcsct multi_outputt y_numerict ensure_2dii˙˙˙˙R(RRN(RRtNonet isinstancetfloatRtFalseRtnpt atleast_1dR tlentshapetreshapeR Rt dual_coef_traveltX_fit_(RRtyt sample_weighttKR R+tcopy((s3lib/python2.7/site-packages/sklearn/kernel_ridge.pytfitƒs$    cCs;t|ddgƒ|j||jƒ}tj||jƒS(s%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*(RRR,R%tdotR*(RRR/((s3lib/python2.7/site-packages/sklearn/kernel_ridge.pytpredict°sN( t__name__t __module__t__doc__R!RRtpropertyRR1R3(((s3lib/python2.7/site-packages/sklearn/kernel_ridge.pyRs[  -(R6tnumpyR%tbaseRRtmetrics.pairwiseRtlinear_model.ridgeRtutilsRRtutils.validationRR(((s3lib/python2.7/site-packages/sklearn/kernel_ridge.pyts