`sklearn.linear_model`.MultiTaskElasticNet¶

class sklearn.linear_model.MultiTaskElasticNet(alpha=1.0, *, l1_ratio=0.5, fit_intercept=True, normalize=False, copy_X=True, max_iter=1000, tol=0.0001, warm_start=False, random_state=None, selection='cyclic')[source]¶

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.

See also

MultiTaskElasticNetCV: 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.

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]

Methods

`fit`(X, y)	Fit MultiTaskElasticNet 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 MultiTaskElasticNet model with coordinate descent

Parameters

Xndarray of shape (n_samples, n_features): Data.
yndarray of shape (n_samples, n_tasks): Target. Will be cast to X’s dtype if necessary.

Notes

Coordinate descent is an algorithm that considers each column of data at a time hence it will automatically convert the X input as a Fortran-contiguous numpy array if necessary.

To avoid memory re-allocation it is advised to allocate the initial data in memory directly using that format.

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.

sklearn.linear_model.MultiTaskElasticNet¶

`sklearn.linear_model`.MultiTaskElasticNet¶