Lasso linear model with iterative fitting along a regularization path.
See glossary entry for :term:`cross-validation estimator`.
The best model is selected by cross-validation.
The optimization objective for Lasso is::
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
Read more in the :ref:`User Guide <lasso>`.
Parameters ---------- eps : float, default=1e-3 Length of the path. ``eps=1e-3`` means that ``alpha_min / alpha_max = 1e-3``.
n_alphas : int, default=100 Number of alphas along the regularization path
alphas : ndarray, default=None List of alphas where to compute the models. If ``None`` alphas are set automatically
fit_intercept : bool, default=True whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
normalize : bool, 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 : 'auto', bool or array-like of shape (n_features, n_features), default='auto' 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.
max_iter : int, default=1000 The maximum number of iterations
tol : float, default=1e-4 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``.
copy_X : bool, default=True If ``True``, X will be copied; else, it may be overwritten.
cv : int, cross-validation generator or iterable, default=None Determines the cross-validation splitting strategy. Possible inputs for cv are:
- None, to use the default 5-fold cross-validation,
- int, to specify the number of folds.
- :term:`CV splitter`,
- An iterable yielding (train, test) splits as arrays of indices.
For int/None inputs, :class:`KFold` is used.
Refer :ref:`User Guide <cross_validation>` for the various cross-validation strategies that can be used here.
.. versionchanged:: 0.22 ``cv`` default value if None changed from 3-fold to 5-fold.
verbose : bool or int, default=False Amount of verbosity.
n_jobs : int, default=None Number of CPUs to use during the cross validation. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary <n_jobs>` for more details.
positive : bool, default=False If positive, restrict regression coefficients to be positive
random_state : int, RandomState instance, default=None The seed of the pseudo random number generator that selects a random feature to update. Used when ``selection`` == 'random'. Pass an int for reproducible output across multiple function calls. See :term:`Glossary <random_state>`.
selection : 'cyclic', 'random'
, 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 ---------- alpha_ : float The amount of penalization chosen by cross validation
coef_ : ndarray of shape (n_features,) or (n_targets, n_features) parameter vector (w in the cost function formula)
intercept_ : float or ndarray of shape (n_targets,) independent term in decision function.
mse_path_ : ndarray of shape (n_alphas, n_folds) mean square error for the test set on each fold, varying alpha
alphas_ : ndarray of shape (n_alphas,) The grid of alphas used for fitting
dual_gap_ : float or ndarray of shape (n_targets,) The dual gap at the end of the optimization for the optimal alpha (``alpha_``).
n_iter_ : int number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.
Examples -------- >>> from sklearn.linear_model import LassoCV >>> from sklearn.datasets import make_regression >>> X, y = make_regression(noise=4, random_state=0) >>> reg = LassoCV(cv=5, random_state=0).fit(X, y) >>> reg.score(X, y) 0.9993... >>> reg.predict(X:1,
) array(-78.4951...
)
Notes ----- For an example, see :ref:`examples/linear_model/plot_lasso_model_selection.py <sphx_glr_auto_examples_linear_model_plot_lasso_model_selection.py>`.
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.
See also -------- lars_path lasso_path LassoLars Lasso LassoLarsCV