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 :ref:`User Guide <elastic_net>`.
Parameters ---------- alpha : float, 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 the :class:`LinearRegression` object. For numerical reasons, using ``alpha = 0`` with the ``Lasso`` object is not advised. Given this, you should use the :class:`LinearRegression` object.
l1_ratio : float The ElasticNet mixing parameter, with ``0 <= l1_ratio <= 1``. For ``l1_ratio = 0`` the penalty is an L2 penalty. ``For l1_ratio = 1`` it is an L1 penalty. For ``0 < l1_ratio < 1``, the penalty is a combination of L1 and L2.
fit_intercept : bool Whether the intercept should be estimated or not. If ``False``, the data is assumed to be already centered.
normalize : boolean, 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 l2-norm. If you wish to standardize, please use :class:`sklearn.preprocessing.StandardScaler` before calling ``fit`` on an estimator with ``normalize=False``.
precompute : True | False | array-like 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_iter : int, optional The maximum number of iterations
copy_X : boolean, optional, default True If ``True``, X will be copied; else, it may be overwritten.
tol : float, 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 than ``tol``.
warm_start : bool, optional When set to ``True``, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See :term:`the Glossary <warm_start>`.
positive : bool, optional When set to ``True``, forces the coefficients to be positive.
random_state : int, 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 when ``selection`` == 'random'.
selection : str, 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 1e-4.
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_coef_`` is a readonly property derived from ``coef_``
intercept_ : float | array, shape (n_targets,) independent term in decision function.
n_iter_ : array-like, shape (n_targets,) number of iterations run by the coordinate descent solver to reach the specified tolerance.
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...
Notes ----- To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.
See also -------- ElasticNetCV : Elastic net model with best model selection by cross-validation. SGDRegressor: implements elastic net regression with incremental training. SGDClassifier: implements logistic regression with elastic net penalty (``SGDClassifier(loss="log", penalty="elasticnet")``).