3.2.4.1.6. `sklearn.linear_model`.MultiTaskElasticNetCV¶

class sklearn.linear_model.MultiTaskElasticNetCV(l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, max_iter=1000, tol=0.0001, cv='warn', copy_X=True, verbose=0, n_jobs=None, random_state=None, selection='cyclic')[source]¶

Multi-task L1/L2 ElasticNet with built-in cross-validation.

See glossary entry for cross-validation estimator.

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 User Guide.

Parameters:

l1_ratio : float or array of floats

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. This parameter can be a list, in which case the different values are tested by cross-validation and the one giving the best prediction score is used. Note that a good choice of list of values for l1_ratio is often to put more values close to 1 (i.e. Lasso) and less close to 0 (i.e. Ridge), as in [.1, .5, .7, .9, .95, .99, 1]

eps : float, optional

Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.

n_alphas : int, optional

Number of alphas along the regularization path

alphas : array-like, optional

List of alphas where to compute the models. If not provided, set automatically.

fit_intercept : boolean

whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected 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 sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.

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.

cv : int, cross-validation generator or an iterable, optional

Determines the cross-validation splitting strategy. Possible inputs for cv are:

None, to use the default 3-fold cross-validation,
integer, to specify the number of folds.
CV splitter,
An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, KFold is used.

Refer User Guide for the various cross-validation strategies that can be used here.

Changed in version 0.20: cv default value if None will change from 3-fold to 5-fold in v0.22.

copy_X : boolean, optional, default True

If True, X will be copied; else, it may be overwritten.

verbose : bool or integer

Amount of verbosity.

n_jobs : int or None, optional (default=None)

Number of CPUs to use during the cross validation. Note that this is used only if multiple values for l1_ratio are given. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

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). Note that coef_ stores the transpose of W, W.T.
alpha_ : float: The amount of penalization chosen by cross validation
mse_path_ : array, shape (n_alphas, n_folds) or (n_l1_ratio, n_alphas, n_folds): mean square error for the test set on each fold, varying alpha
alphas_ : numpy array, shape (n_alphas,) or (n_l1_ratio, n_alphas): The grid of alphas used for fitting, for each l1_ratio
l1_ratio_ : float: best l1_ratio obtained by cross-validation.
n_iter_ : int: number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.

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.

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.MultiTaskElasticNetCV(cv=3)
>>> clf.fit([[0,0], [1, 1], [2, 2]],
...         [[0, 0], [1, 1], [2, 2]])
... #doctest: +NORMALIZE_WHITESPACE
MultiTaskElasticNetCV(alphas=None, copy_X=True, cv=3, eps=0.001,
       fit_intercept=True, l1_ratio=0.5, max_iter=1000, n_alphas=100,
       n_jobs=None, normalize=False, random_state=None, selection='cyclic',
       tol=0.0001, verbose=0)
>>> print(clf.coef_)
[[0.52875032 0.46958558]
 [0.52875032 0.46958558]]
>>> print(clf.intercept_)
[0.00166409 0.00166409]

Methods

`fit`(X, y)	Fit linear model with coordinate descent
`get_params`([deep])	Get parameters for this estimator.
`path`(X, y[, l1_ratio, eps, n_alphas, …])	Compute elastic net path with coordinate descent
`predict`(X)	Predict using the linear model
`score`(X, y[, sample_weight])	Returns the coefficient of determination R^2 of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

__init__(l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, max_iter=1000, tol=0.0001, cv='warn', copy_X=True, verbose=0, n_jobs=None, random_state=None, selection='cyclic')[source]¶: Initialize self. See help(type(self)) for accurate signature.

fit(X, y)[source]¶

Fit linear model with coordinate descent

Fit is on grid of alphas and best alpha estimated by cross-validation.

Parameters:	X : {array-like}, shape (n_samples, n_features) Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output, X can be sparse. y : array-like, shape (n_samples,) or (n_samples, n_targets) Target values

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters:	deep : boolean, optional If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:	params : mapping 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 multi-outputs.

For mono-output 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 multi-output 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.

Parameters:	X : array_like or sparse matrix, shape (n_samples, n_features) Samples.
Returns:	C : array, shape (n_samples,) Returns predicted values.

3.2.4.1.6. sklearn.linear_model.MultiTaskElasticNetCV¶

3.2.4.1.6. `sklearn.linear_model`.MultiTaskElasticNetCV¶