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=None, 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.  New in version 0.15.   Parameters 
 
l1_ratiofloat or list of 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. 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]  
epsfloat, default=1e-3 

Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.  
n_alphasint, default=100 

Number of alphas along the regularization path.  
alphasarray-like, default=None 

List of alphas where to compute the models. If not provided, set automatically.  
fit_interceptbool, 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).  
normalizebool, 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 StandardScaler before calling fit on an estimator with normalize=False.  
max_iterint, default=1000 

The maximum number of iterations.  
tolfloat, 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.  
cvint, 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. 
CV splitter, An iterable yielding (train, test) splits as arrays of indices.  For int/None inputs, KFold is used. Refer User Guide for the various cross-validation strategies that can be used here.  Changed in version 0.22: cv default value if None changed from 3-fold to 5-fold.   
copy_Xbool, default=True 

If True, X will be copied; else, it may be overwritten.  
verbosebool or int, default=0 

Amount of verbosity.  
n_jobsint, 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_stateint, 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 Glossary.  
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). Note that coef_ stores the transpose of W, W.T.  
alpha_float 

The amount of penalization chosen by cross validation.  
mse_path_ndarray of 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_ndarray of 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.  
dual_gap_float 

The dual gap at the end of the optimization for the optimal alpha.      See also  
MultiTaskElasticNet


ElasticNetCV


MultiTaskLassoCV

  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. 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(cv=3)
>>> 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(*args, **kwargs) Compute elastic net path with coordinate descent.  
predict(X) Predict using the linear model.  
score(X, y[, sample_weight]) Return the coefficient of determination \(R^2\) of the prediction.  
set_params(**params) Set the parameters of this estimator.    
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, sparse matrix} of 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.  
yarray-like of shape (n_samples,) or (n_samples, n_targets) 

Target values.     
  
get_params(deep=True) [source]
 
Get parameters for this estimator.  Parameters 
 
deepbool, default=True 

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns 
 
paramsdict 

Parameter names mapped to their values.     
  
static path(*args, **kwargs) [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. Read more in the User Guide.  Parameters 
 
X{array-like, sparse matrix} of shape (n_samples, n_features) 

Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output then X can be sparse.  
y{array-like, sparse matrix} of shape (n_samples,) or (n_samples, n_outputs) 

Target values.  
l1_ratiofloat, default=0.5 

Number between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). l1_ratio=1 corresponds to the Lasso.  
epsfloat, default=1e-3 

Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.  
n_alphasint, default=100 

Number of alphas along the regularization path.  
alphasndarray, default=None 

List of alphas where to compute the models. If None alphas are set automatically.  
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.  
Xyarray-like of shape (n_features,) or (n_features, n_outputs), default=None 

Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.  
copy_Xbool, default=True 

If True, X will be copied; else, it may be overwritten.  
coef_initndarray of shape (n_features, ), default=None 

The initial values of the coefficients.  
verbosebool or int, default=False 

Amount of verbosity.  
return_n_iterbool, default=False 

Whether to return the number of iterations or not.  
positivebool, default=False 

If set to True, forces coefficients to be positive. (Only allowed when y.ndim == 1).  
check_inputbool, default=True 

If set to False, the input validation checks are skipped (including the Gram matrix when provided). It is assumed that they are handled by the caller.  
**paramskwargs 

Keyword arguments passed to the coordinate descent solver.    Returns 
 
alphasndarray of shape (n_alphas,) 

The alphas along the path where models are computed.  
coefsndarray of shape (n_features, n_alphas) or (n_outputs, n_features, n_alphas) 

Coefficients along the path.  
dual_gapsndarray of shape (n_alphas,) 

The dual gaps at the end of the optimization for each alpha.  
n_iterslist of int 

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).      See also  
MultiTaskElasticNet


MultiTaskElasticNetCV


ElasticNet


ElasticNetCV

  Notes For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py. 
  
predict(X) [source]
 
Predict using the linear model.  Parameters 
 
Xarray-like or sparse matrix, shape (n_samples, n_features) 

Samples.    Returns 
 
Carray, shape (n_samples,) 

Returns predicted values.     
  
score(X, y, sample_weight=None) [source]
 
Return the coefficient of determination \(R^2\) of the prediction. The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), 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 
 
Xarray-like of shape (n_samples, n_features) 

Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.  
yarray-like of shape (n_samples,) or (n_samples, n_outputs) 

True values for X.  
sample_weightarray-like of shape (n_samples,), default=None 

Sample weights.    Returns 
 
scorefloat 

\(R^2\) of self.predict(X) wrt. y.     Notes The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor). 
  
set_params(**params) [source]
 
Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.  Parameters 
 
**paramsdict 

Estimator parameters.    Returns 
 
selfestimator instance 

Estimator instance.