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 norm of each row.
Read more in the :ref:`User Guide <multi_task_elastic_net>`.
Parameters ---------- alpha : float, optional Constant that multiplies the L1/L2 term. Defaults to 1.0
l1_ratio : float 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 : boolean 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 : 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``.
copy_X : boolean, optional, default True If ``True``, X will be copied; else, it may be overwritten.
max_iter : int, optional The maximum number of iterations
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>`.
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 ---------- intercept_ : array, shape (n_tasks,) Independent term in decision function.
coef_ : array, 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 argument of the fit method should be directly passed as a Fortran-contiguous numpy array.