sklearn.linear_model
.Ridge¶
- class sklearn.linear_model.Ridge(alpha=1.0, *, fit_intercept=True, normalize='deprecated', copy_X=True, max_iter=None, tol=0.001, solver='auto', random_state=None)[source]¶
Linear least squares with l2 regularization.
Minimizes the objective function:
||y - Xw||^2_2 + alpha * ||w||^2_2
This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm. Also known as Ridge Regression or Tikhonov regularization. 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 User Guide.
- Parameters
- alpha{float, ndarray 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 asLogisticRegression
orLinearSVC
. If an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number.- fit_interceptbool, default=True
Whether to fit the intercept for this model. If set to false, no intercept will be used in calculations (i.e.
X
andy
are expected to be centered).- normalizebool, default=False
This parameter is ignored when
fit_intercept
is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please useStandardScaler
before callingfit
on an estimator withnormalize=False
.Deprecated since version 1.0:
normalize
was deprecated in version 1.0 and will be removed in 1.2.- copy_Xbool, default=True
If True, X will be copied; else, it may be overwritten.
- max_iterint, default=None
Maximum number of iterations for conjugate gradient solver. For ‘sparse_cg’ and ‘lsqr’ solvers, the default value is determined by scipy.sparse.linalg. For ‘sag’ solver, the default value is 1000.
- tolfloat, default=1e-3
Precision of the solution.
- solver{‘auto’, ‘svd’, ‘cholesky’, ‘lsqr’, ‘sparse_cg’, ‘sag’, ‘saga’}, default=’auto’
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
andmax_iter
).‘lsqr’ uses the dedicated regularized least-squares routine scipy.sparse.linalg.lsqr. It is the fastest and uses an iterative procedure.
‘sag’ uses a Stochastic Average Gradient descent, and ‘saga’ uses its improved, unbiased version named SAGA. Both methods also use an iterative procedure, and are often faster than other solvers when both n_samples and n_features are large. Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.
All last five solvers support both dense and sparse data. However, only ‘sag’ and ‘sparse_cg’ supports sparse input when
fit_intercept
is True.New in version 0.17: Stochastic Average Gradient descent solver.
New in version 0.19: SAGA solver.
- random_stateint, RandomState instance, default=None
Used when
solver
== ‘sag’ or ‘saga’ to shuffle the data. See Glossary for details.New in version 0.17:
random_state
to support Stochastic Average Gradient.
- Attributes
- coef_ndarray of shape (n_features,) or (n_targets, n_features)
Weight vector(s).
- intercept_float or ndarray of shape (n_targets,)
Independent term in decision function. Set to 0.0 if
fit_intercept = False
.- n_iter_None or ndarray of shape (n_targets,)
Actual number of iterations for each target. Available only for sag and lsqr solvers. Other solvers will return None.
New in version 0.17.
- n_features_in_int
Number of features seen during fit.
New in version 0.24.
See also
RidgeClassifier
Ridge classifier.
RidgeCV
Ridge regression with built-in cross validation.
KernelRidge
Kernel ridge regression combines ridge regression with the kernel trick.
Examples
>>> from sklearn.linear_model import Ridge >>> 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 = Ridge(alpha=1.0) >>> clf.fit(X, y) Ridge()
Methods
fit
(X, y[, sample_weight])Fit Ridge regression model.
get_params
([deep])Get parameters for this estimator.
predict
(X)Predict using the linear model.
score
(X, y[, sample_weight])Return the coefficient of determination \(R^2\) of the prediction.
set_params
(**params)Set the parameters of this estimator.
- fit(X, y, sample_weight=None)[source]¶
Fit Ridge regression model.
- Parameters
- X{ndarray, sparse matrix} of shape (n_samples, n_features)
Training data
- yndarray of shape (n_samples,) or (n_samples, n_targets)
Target values
- sample_weightfloat or ndarray of shape (n_samples,), default=None
Individual weights for each sample. If given a float, every sample will have the same weight.
- Returns
- selfreturns an instance of self.
- get_params(deep=True)[source]¶
Get parameters for this estimator.
- Parameters
- deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
- Returns
- paramsdict
Parameter names mapped to their values.
- predict(X)[source]¶
Predict using the linear model.
- Parameters
- Xarray-like or sparse matrix, shape (n_samples, n_features)
Samples.
- Returns
- Carray, shape (n_samples,)
Returns predicted values.
- score(X, y, sample_weight=None)[source]¶
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares
((y_true - y_pred) ** 2).sum()
and \(v\) is the total sum of squares((y_true - y_true.mean()) ** 2).sum()
. The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value ofy
, disregarding the input features, would get a \(R^2\) score of 0.0.- Parameters
- Xarray-like of shape (n_samples, n_features)
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape
(n_samples, n_samples_fitted)
, wheren_samples_fitted
is the number of samples used in the fitting for the estimator.- yarray-like of shape (n_samples,) or (n_samples, n_outputs)
True values for
X
.- sample_weightarray-like of shape (n_samples,), default=None
Sample weights.
- Returns
- scorefloat
\(R^2\) of
self.predict(X)
wrt.y
.
Notes
The \(R^2\) score used when calling
score
on a regressor usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).
- set_params(**params)[source]¶
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as
Pipeline
). The latter have parameters of the form<component>__<parameter>
so that it’s possible to update each component of a nested object.- Parameters
- **paramsdict
Estimator parameters.
- Returns
- selfestimator instance
Estimator instance.