Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer
The optimization objective for MultiTaskElasticNet 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 norms of each row.
Read more in the :ref:`User Guide <multi_task_elastic_net>`.
Parameters ---------- alpha : float, default=1.0 Constant that multiplies the L1/L2 term. Defaults to 1.0
l1_ratio : float, default=0.5 The ElasticNet mixing parameter, with 0 < l1_ratio <= 1. For l1_ratio = 1 the penalty is an L1/L2 penalty. For l1_ratio = 0 it is an L2 penalty. For ``0 < l1_ratio < 1``, the penalty is a combination of L1/L2 and L2.
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``.
copy_X : bool, default=True If ``True``, X will be copied; else, it may be overwritten.
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``.
warm_start : bool, default=False 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>`.
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 ---------- intercept_ : ndarray of shape (n_tasks,) Independent term in decision function.
coef_ : ndarray of shape (n_tasks, n_features) Parameter vector (W in the cost function formula). If a 1D y is passed in at fit (non multi-task usage), ``coef_`` is then a 1D array. Note that ``coef_`` stores the transpose of ``W``, ``W.T``.
n_iter_ : int number of iterations run by the coordinate descent solver to reach the specified tolerance.
Examples -------- >>> from sklearn import linear_model >>> clf = linear_model.MultiTaskElasticNet(alpha=0.1) >>> clf.fit([0,0], [1, 1], [2, 2]
, [0, 0], [1, 1], [2, 2]
) MultiTaskElasticNet(alpha=0.1) >>> print(clf.coef_) [0.45663524 0.45612256]
[0.45663524 0.45612256]
>>> print(clf.intercept_) 0.0872422 0.0872422
See also -------- MultiTaskElasticNet : Multi-task L1/L2 ElasticNet with built-in cross-validation. ElasticNet MultiTaskLasso
Notes ----- The algorithm used to fit the model is coordinate descent.
To avoid unnecessary memory duplication the X and y arguments of the fit method should be directly passed as Fortran-contiguous numpy arrays.