scikit-learn linearRegression 1.1.2 岭回归

>>> from sklearn import linear_model
>>> clf = linear_model.Ridge (alpha = .5)
>>> clf.fit ([[0, 0], [0, 0], [1, 1]], [0, .1, 1]) 
Ridge(alpha=0.5, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
>>> clf.coef_
array([ 0.34545455,  0.34545455])
>>> clf.intercept_ 
0.13636...

绘制岭系数正则化的函数

岭回归是本例中使用的估计量，美中衍射代表不同系数向量特征，在路径末端，alpha趋于零，解趋于普通最小二乘法，系数表现出现很大的震荡

# Author: Fabian Pedregosa -- <fabian.pedregosa@inria.fr>
# License: BSD 3 clauseprint(__doc__)import numpy as np
import matplotlib.pyplot as plt
from sklearn import linear_model# X is the 10x10 Hilbert matrix 希尔伯特矩阵
X = 1. / (np.arange(1, 11) + np.arange(0, 10)[:, np.newaxis])
y = np.ones(10)###############################################################################
# Compute paths a为alpha 正则化系数，通过便利-10 到 -2之间200个系数，来寻找最佳系数n_alphas = 200
alphas = np.logspace(-10, -2, n_alphas)
clf = linear_model.Ridge(fit_intercept=False)coefs = []
for a in alphas:clf.set_params(alpha=a)clf.fit(X, y)coefs.append(clf.coef_)###############################################################################
# Display resultsax = plt.gca()
ax.set_color_cycle(['b', 'r', 'g', 'c', 'k', 'y', 'm'])ax.plot(alphas, coefs)
ax.set_xscale('log')
ax.set_xlim(ax.get_xlim()[::-1])  # reverse axis
plt.xlabel('alpha')
plt.ylabel('weights')
plt.title('Ridge coefficients as a function of the regularization')
plt.axis('tight')
plt.show()

   class sklearn.linear_model.RidgeClassifier(alpha=1.0, fit_intercept=True, normalize=False, copy_X=True, max_iter=None, tol=0.001, class_weight=None, solver='auto', random_state=None)[source]
Classifier using Ridge regression.
Read more in the User Guide.
Parameters:
alpha : float
 
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 C^-1 in other linear models such as LogisticRegression or LinearSVC.
 
class_weight : dict or ‘balanced’, optional
 
Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one.
 
The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y))
 
copy_X : boolean, optional, default True
 
If True, X will be copied; else, it may be overwritten.
 
fit_intercept : boolean
 
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).
 
max_iter : int, optional
 
Maximum number of iterations for conjugate gradient solver. The default value is determined by scipy.sparse.linalg.
 
normalize : boolean, optional, default False
 
If True, the regressors X will be normalized before regression. This parameter is ignored when fit_intercept is set to False. When the regressors are normalized, note that this makes the hyperparameters learnt more robust and almost independent of the number of samples. The same property is not valid for standardized data. However, if you wish to standardize, please use preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
 
solver : {‘auto’, ‘svd’, ‘cholesky’, ‘lsqr’, ‘sparse_cg’, ‘sag’}
 
Solver to use in the computational routines:
 
‘auto’ chooses the solver automatically based on the type of data.
‘svd’ uses a Singular Value Decomposition of X to compute the Ridge coefficients. More stable for singular matrices than ‘cholesky’.
‘cholesky’ uses the standard scipy.linalg.solve function to obtain a closed-form solution.
‘sparse_cg’ uses the conjugate gradient solver as found in scipy.sparse.linalg.cg. As an iterative algorithm, this solver is more appropriate than ‘cholesky’ for large-scale data (possibility to set tol and max_iter).
‘lsqr’ uses the dedicated regularized least-squares routine scipy.sparse.linalg.lsqr. It is the fastest but may not be available in old scipy versions. It also uses an iterative procedure.
‘sag’ uses a Stochastic Average Gradient descent. It also uses an iterative procedure, and is faster than other solvers when both n_samples and n_features are large.
 
 
New in version 0.17: Stochastic Average Gradient descent solver.
 
 
tol : float
 
Precision of the solution.
 
random_state : int seed, RandomState instance, or None (default)
 
The seed of the pseudo random number generator to use when shuffling the data. Used in ‘sag’ solver.
 
Attributes:
coef_ : array, shape (n_features,) or (n_classes, n_features)
 
Weight vector(s).
 
intercept_ : float | array, shape = (n_targets,)
 
Independent term in decision function. Set to 0.0 if fit_intercept = False.
 
n_iter_ : array or None, shape (n_targets,)
 
Actual number of iterations for each target. Available only for sag and lsqr solvers. Other solvers will return None.
 
See also
 
Ridge, RidgeClassifierCV
Notes
For multi-class classification, n_class classifiers are trained in a one-versus-all approach. Concretely, this is implemented by taking advantage of the multi-variate response support in Ridge.
Methods
decision_function(X)
Predict
confidence scores for samples.
fit(X, y[, sample_weight])
Fit
Ridge regression model.
get_params([deep])
Get
parameters for this estimator.
predict(X)
Predict
class labels for samples in X.
score(X, y[, sample_weight])
Returns
the mean accuracy on the given test data and labels.
set_params(\*\*params)
Set
the parameters of this estimator.
__init__(alpha=1.0, fit_intercept=True, normalize=False, copy_X=True, max_iter=None, tol=0.001, class_weight=None, solver='auto', random_state=None)[source]
decision_function(X)[source]
Predict confidence scores for samples.
The confidence score for a sample is the signed distance of that sample to the hyperplane.
Parameters:
X : {array-like, sparse matrix}, shape = (n_samples, n_features)
 
 
Samples.
 
Returns:
array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes) :
 
 
Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.
 
fit(X, y, sample_weight=None)[source]
Fit Ridge regression model.
Parameters:
X : {array-like, sparse matrix}, shape = [n_samples,n_features]
 
 
Training data
 
y : array-like, shape = [n_samples]
 
 
Target values
 
sample_weight : float or numpy array of shape (n_samples,)
 
 
Sample weight.
 
 
New in version 0.17: sample_weight support to Classifier.
 
 
Returns:
self : returns an instance of self.
get_params(deep=True)[source]
Get parameters for this estimator.
Parameters:
deep : boolean, optional
 
 
If True, will return the parameters for this estimator and contained subobjects that are estimators.
 
Returns:
params : mapping of string to any
 
 
Parameter names mapped to their values.
 
predict(X)[source]
Predict class labels for samples in X.
Parameters:
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
 
 
Samples.
 
Returns:
C : array, shape = [n_samples]
 
 
Predicted class label per sample.
 
score(X, y, sample_weight=None)[source]
Returns the mean accuracy on the given test data and labels.
In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.
Parameters:
X : array-like, shape = (n_samples, n_features)
 
 
Test samples.
 
y : array-like, shape = (n_samples) or (n_samples, n_outputs)
 
 
True labels for X.
 
sample_weight : array-like, shape = [n_samples], optional
 
 
Sample weights.
 
Returns:
score : float
 
 
Mean accuracy of self.predict(X) wrt. y.
 
set_params(**params)[source]
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

文章参考：http://blog.csdn.net/google19890102/article/details/27228279