sklearn.linear_model
.ElasticNet¶

class
sklearn.linear_model.
ElasticNet
(alpha=1.0, l1_ratio=0.5, fit_intercept=True, normalize=False, precompute=False, max_iter=1000, copy_X=True, tol=0.0001, warm_start=False, positive=False, random_state=None, selection='cyclic')[source]¶ Linear regression with combined L1 and L2 priors as regularizer.
Minimizes the objective function:
1 / (2 * n_samples) * y  Xw^2_2 + alpha * l1_ratio * w_1 + 0.5 * alpha * (1  l1_ratio) * w^2_2
If you are interested in controlling the L1 and L2 penalty separately, keep in mind that this is equivalent to:
a * L1 + b * L2
where:
alpha = a + b and l1_ratio = a / (a + b)
The parameter l1_ratio corresponds to alpha in the glmnet R package while alpha corresponds to the lambda parameter in glmnet. Specifically, l1_ratio = 1 is the lasso penalty. Currently, l1_ratio <= 0.01 is not reliable, unless you supply your own sequence of alpha.
Read more in the User Guide.
 Parameters
 alphafloat, optional
Constant that multiplies the penalty terms. Defaults to 1.0. See the notes for the exact mathematical meaning of this parameter.
alpha = 0
is equivalent to an ordinary least square, solved by theLinearRegression
object. For numerical reasons, usingalpha = 0
with theLasso
object is not advised. Given this, you should use theLinearRegression
object. l1_ratiofloat
The ElasticNet mixing parameter, with
0 <= l1_ratio <= 1
. Forl1_ratio = 0
the penalty is an L2 penalty.For l1_ratio = 1
it is an L1 penalty. For0 < l1_ratio < 1
, the penalty is a combination of L1 and L2. fit_interceptbool
Whether the intercept should be estimated or not. If
False
, the data is assumed to be already centered. normalizeboolean, optional, 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 l2norm. If you wish to standardize, please usesklearn.preprocessing.StandardScaler
before callingfit
on an estimator withnormalize=False
. precomputeTrue  False  arraylike
Whether to use a precomputed Gram matrix to speed up calculations. The Gram matrix can also be passed as argument. For sparse input this option is always
True
to preserve sparsity. max_iterint, optional
The maximum number of iterations
 copy_Xboolean, optional, default True
If
True
, X will be copied; else, it may be overwritten. tolfloat, optional
The tolerance for the optimization: if the updates are smaller than
tol
, the optimization code checks the dual gap for optimality and continues until it is smaller thantol
. warm_startbool, optional
When set to
True
, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary. positivebool, optional
When set to
True
, forces the coefficients to be positive. random_stateint, RandomState instance or None, optional, default None
The seed of the pseudo random number generator that selects a random feature to update. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by
np.random
. Used whenselection
== ‘random’. selectionstr, default ‘cyclic’
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e4.
 Attributes
 coef_array, shape (n_features,)  (n_targets, n_features)
parameter vector (w in the cost function formula)
sparse_coef_
scipy.sparse matrix, shape (n_features, 1)  (n_targets, n_features)sparse representation of the fitted
coef_
 intercept_float  array, shape (n_targets,)
independent term in decision function.
 n_iter_arraylike, shape (n_targets,)
number of iterations run by the coordinate descent solver to reach the specified tolerance.
See also
ElasticNetCV
Elastic net model with best model selection by crossvalidation.
SGDRegressor
implements elastic net regression with incremental training.
SGDClassifier
implements logistic regression with elastic net penalty (
SGDClassifier(loss="log", penalty="elasticnet")
).
Notes
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortrancontiguous numpy array.
Examples
>>> from sklearn.linear_model import ElasticNet >>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=2, random_state=0) >>> regr = ElasticNet(random_state=0) >>> regr.fit(X, y) ElasticNet(random_state=0) >>> print(regr.coef_) [18.83816048 64.55968825] >>> print(regr.intercept_) 1.451... >>> print(regr.predict([[0, 0]])) [1.451...]
Methods
fit
(self, X, y[, check_input])Fit model with coordinate descent.
get_params
(self[, deep])Get parameters for this estimator.
path
(X, y[, l1_ratio, eps, n_alphas, …])Compute elastic net path with coordinate descent
predict
(self, X)Predict using the linear model
score
(self, X, y[, sample_weight])Returns the coefficient of determination R^2 of the prediction.
set_params
(self, \*\*params)Set the parameters of this estimator.

__init__
(self, alpha=1.0, l1_ratio=0.5, fit_intercept=True, normalize=False, precompute=False, max_iter=1000, copy_X=True, tol=0.0001, warm_start=False, positive=False, random_state=None, selection='cyclic')[source]¶ Initialize self. See help(type(self)) for accurate signature.

fit
(self, X, y, check_input=True)[source]¶ Fit model with coordinate descent.
 Parameters
 Xndarray or scipy.sparse matrix, (n_samples, n_features)
Data
 yndarray, shape (n_samples,) or (n_samples, n_targets)
Target. Will be cast to X’s dtype if necessary
 check_inputboolean, (default=True)
Allow to bypass several input checking. Don’t use this parameter unless you know what you do.
Notes
Coordinate descent is an algorithm that considers each column of data at a time hence it will automatically convert the X input as a Fortrancontiguous numpy array if necessary.
To avoid memory reallocation it is advised to allocate the initial data in memory directly using that format.

get_params
(self, deep=True)[source]¶ Get parameters for this estimator.
 Parameters
 deepboolean, optional
If True, will return the parameters for this estimator and contained subobjects that are estimators.
 Returns
 paramsmapping of string to any
Parameter names mapped to their values.

static
path
(X, y, l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, precompute='auto', Xy=None, copy_X=True, coef_init=None, verbose=False, return_n_iter=False, positive=False, check_input=True, **params)[source]¶ Compute elastic net path with coordinate descent
The elastic net optimization function varies for mono and multioutputs.
For monooutput tasks it is:
1 / (2 * n_samples) * y  Xw^2_2 + alpha * l1_ratio * w_1 + 0.5 * alpha * (1  l1_ratio) * w^2_2
For multioutput tasks it is:
(1 / (2 * n_samples)) * Y  XW^Fro_2 + alpha * l1_ratio * W_21 + 0.5 * alpha * (1  l1_ratio) * W_Fro^2
Where:
W_21 = \sum_i \sqrt{\sum_j w_{ij}^2}
i.e. the sum of norm of each row.
Read more in the User Guide.
 Parameters
 X{arraylike}, shape (n_samples, n_features)
Training data. Pass directly as Fortrancontiguous data to avoid unnecessary memory duplication. If
y
is monooutput thenX
can be sparse. yndarray, shape (n_samples,) or (n_samples, n_outputs)
Target values
 l1_ratiofloat, optional
float between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties).
l1_ratio=1
corresponds to the Lasso epsfloat
Length of the path.
eps=1e3
means thatalpha_min / alpha_max = 1e3
 n_alphasint, optional
Number of alphas along the regularization path
 alphasndarray, optional
List of alphas where to compute the models. If None alphas are set automatically
 precomputeTrue  False  ‘auto’  arraylike
Whether to use a precomputed Gram matrix to speed up calculations. If set to
'auto'
let us decide. The Gram matrix can also be passed as argument. Xyarraylike, optional
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
 copy_Xboolean, optional, default True
If
True
, X will be copied; else, it may be overwritten. coef_initarray, shape (n_features, )  None
The initial values of the coefficients.
 verbosebool or integer
Amount of verbosity.
 return_n_iterbool
whether to return the number of iterations or not.
 positivebool, default False
If set to True, forces coefficients to be positive. (Only allowed when
y.ndim == 1
). check_inputbool, default True
Skip input validation checks, including the Gram matrix when provided assuming there are handled by the caller when check_input=False.
 **paramskwargs
keyword arguments passed to the coordinate descent solver.
 Returns
 alphasarray, shape (n_alphas,)
The alphas along the path where models are computed.
 coefsarray, shape (n_features, n_alphas) or (n_outputs, n_features, n_alphas)
Coefficients along the path.
 dual_gapsarray, shape (n_alphas,)
The dual gaps at the end of the optimization for each alpha.
 n_itersarraylike, shape (n_alphas,)
The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha. (Is returned when
return_n_iter
is set to True).
Notes
For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.

predict
(self, 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
(self, X, y, sample_weight=None)[source]¶ Returns the coefficient of determination R^2 of the prediction.
The coefficient R^2 is defined as (1  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 of y, disregarding the input features, would get a R^2 score of 0.0.
 Parameters
 Xarraylike, shape = (n_samples, n_features)
Test samples. For some estimators this may be a precomputed kernel matrix instead, shape = (n_samples, n_samples_fitted], where n_samples_fitted is the number of samples used in the fitting for the estimator.
 yarraylike, shape = (n_samples) or (n_samples, n_outputs)
True values for X.
 sample_weightarraylike, shape = [n_samples], optional
Sample weights.
 Returns
 scorefloat
R^2 of self.predict(X) wrt. y.
Notes
The R2 score used when calling
score
on a regressor will usemultioutput='uniform_average'
from version 0.23 to keep consistent withr2_score
. This will influence thescore
method of all the multioutput regressors (except forMultiOutputRegressor
). To specify the default value manually and avoid the warning, please either callr2_score
directly or make a custom scorer withmake_scorer
(the builtin scorer'r2'
usesmultioutput='uniform_average'
).

set_params
(self, **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. Returns
 self

property
sparse_coef_
¶ sparse representation of the fitted
coef_