# MultiTaskElasticNet¶

class ibex.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')

Bases: sklearn.linear_model.coordinate_descent.MultiTaskElasticNet, ibex._base.FrameMixin

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

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 User Guide.

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 (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.
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.
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.
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.
>>> from sklearn import linear_model
>>> clf.fit([[0,0], [1, 1], [2, 2]], [[0, 0], [1, 1], [2, 2]])
...
l1_ratio=0.5, max_iter=1000, normalize=False, random_state=None,
selection='cyclic', tol=0.0001, warm_start=False)
>>> print(clf.coef_)
[[ 0.45663524  0.45612256]
[ 0.45663524  0.45612256]]
>>> print(clf.intercept_)
[ 0.0872422  0.0872422]


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.

fit(X, y)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Fit MultiTaskElasticNet model with coordinate descent

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

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.

predict(X)

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Predict using the linear model

X : {array-like, sparse matrix}, shape = (n_samples, n_features)
Samples.
C : array, shape = (n_samples,)
Returns predicted values.
score(X, y, sample_weight=None)

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

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.

X : array-like, shape = (n_samples, n_features)
Test samples.
y : array-like, shape = (n_samples) or (n_samples, n_outputs)
True values for X.
sample_weight : array-like, shape = [n_samples], optional
Sample weights.
score : float
R^2 of self.predict(X) wrt. y.