Multitask L1/L2 ElasticNet with builtin crossvalidation.
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 crossvalidation 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=1e3 means that alpha_min / alpha_max = 1e3 . 
n_alphas : int, optional 
Number of alphas along the regularization path 
alphas : arraylike, 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 l2norm. 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, crossvalidation generator or an iterable, optional 
Determines the crossvalidation splitting strategy. Possible inputs for cv are:  None, to use the default 3fold crossvalidation,
 integer, to specify the number of folds.
 An object to be used as a crossvalidation generator.
 An iterable yielding train/test splits.
For integer/None inputs, KFold is used. Refer User Guide for the various crossvalidation strategies that can be used here. Changed in version 0.20: cv default value if None will change from 3fold to 5fold 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 1e4. 
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 crossvalidation. 
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 Fortrancontiguous 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]])
...
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]

fit(X, y)
[source]

Fit linear model with coordinate descent
Fit is on grid of alphas and best alpha estimated by crossvalidation.
Parameters: 

X : {arraylike}, shape (n_samples, n_features) 
Training data. Pass directly as Fortrancontiguous data to avoid unnecessary memory duplication. If y is monooutput, X can be sparse. 
y : arraylike, 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 multioutputs.
For monooutput 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 multioutput 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.
Read more in the User Guide.
Parameters: 

X : {arraylike}, shape (n_samples, n_features) 
Training data. Pass directly as Fortrancontiguous data to avoid unnecessary memory duplication. If y is monooutput then X can be sparse. 
y : ndarray, shape (n_samples,) or (n_samples, n_outputs) 
Target values 
l1_ratio : float, optional 
float between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). l1_ratio=1 corresponds to the Lasso 
eps : float 
Length of the path. eps=1e3 means that alpha_min / alpha_max = 1e3 
n_alphas : int, optional 
Number of alphas along the regularization path 
alphas : ndarray, optional 
List of alphas where to compute the models. If None alphas are set automatically 
precompute : True  False  ‘auto’  arraylike 
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. 
Xy : arraylike, optional 
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed. 
copy_X : boolean, optional, default True 
If True , X will be copied; else, it may be overwritten. 
coef_init : array, shape (n_features, )  None 
The initial values of the coefficients. 
verbose : bool or integer 
Amount of verbosity. 
return_n_iter : bool 
whether to return the number of iterations or not. 
positive : bool, default False 
If set to True, forces coefficients to be positive. (Only allowed when y.ndim == 1 ). 
check_input : bool, default True 
Skip input validation checks, including the Gram matrix when provided assuming there are handled by the caller when check_input=False. 
**params : kwargs 
keyword arguments passed to the coordinate descent solver. 
Returns: 

alphas : array, shape (n_alphas,) 
The alphas along the path where models are computed. 
coefs : array, shape (n_features, n_alphas) or (n_outputs, n_features, n_alphas) 
Coefficients along the path. 
dual_gaps : array, shape (n_alphas,) 
The dual gaps at the end of the optimization for each alpha. 
n_iters : arraylike, shape (n_alphas,) 
The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha. (Is returned when return_n_iter is set to True). 
Notes
For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.

predict(X)
[source]

Predict using the linear model
Parameters: 

X : array_like or sparse matrix, shape (n_samples, n_features) 
Samples. 
Returns: 

C : array, shape (n_samples,) 
Returns predicted values. 

score(X, y, sample_weight=None)
[source]

Returns the coefficient of determination R^2 of the prediction.
The coefficient R^2 is defined as (1  u/v), where u is the residual sum of squares ((y_true  y_pred) ** 2).sum() and v is the total sum of squares ((y_true  y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.
Parameters: 

X : arraylike, shape = (n_samples, n_features) 
Test samples. For some estimators this may be a precomputed kernel matrix instead, shape = (n_samples, n_samples_fitted], where n_samples_fitted is the number of samples used in the fitting for the estimator. 
y : arraylike, shape = (n_samples) or (n_samples, n_outputs) 
True values for X. 
sample_weight : arraylike, shape = [n_samples], optional 
Sample weights. 
Returns: 

score : float 
R^2 of self.predict(X) wrt. y. 

set_params(**params)
[source]

Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter>
so that it’s possible to update each component of a nested object.