3.2.4.1.7. `sklearn.linear_model`.MultiTaskLassoCV¶

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

Multi-task Lasso model trained with L1/L2 mixed-norm as regularizer.

See glossary entry for cross-validation estimator.

The optimization objective for MultiTaskLasso is:

(1 / (2 * n_samples)) * ||Y - XW||^Fro_2 + alpha * ||W||_21

Where:

||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}

i.e. the sum of norm of each row.

See also

MultiTaskElasticNet
ElasticNetCV
MultiTaskElasticNetCV

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.linear_model import MultiTaskLassoCV
>>> from sklearn.datasets import make_regression
>>> from sklearn.metrics import r2_score
>>> X, y = make_regression(n_targets=2, noise=4, random_state=0)
>>> reg = MultiTaskLassoCV(cv=5, random_state=0).fit(X, y)
>>> r2_score(y, reg.predict(X))
0.9994...
>>> reg.alpha_
0.5713...
>>> reg.predict(X[:1,])
array([[153.7971...,  94.9015...]])

Methods

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

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

fit(self, 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.
yarray-like, shape (n_samples,) or (n_samples, n_targets): Target values

get_params(self, deep=True)[source]¶

Get parameters for this estimator.

Parameters

deepboolean, optional: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

paramsmapping of string to any: Parameter names mapped to their values.

static path(X, y, 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, **params)[source]¶

Compute Lasso path with coordinate descent

The Lasso optimization function varies for mono and multi-outputs.

For mono-output tasks it is:

(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1

For multi-output tasks it is:

(1 / (2 * n_samples)) * ||Y - XW||^2_Fro + alpha * ||W||_21

Where:

||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}

i.e. the sum of norm of each row.

See also

lars_path
Lasso
LassoLars
LassoCV
LassoLarsCV
sklearn.decomposition.sparse_encode

Notes

For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.

To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

Note that in certain cases, the Lars solver may be significantly faster to implement this functionality. In particular, linear interpolation can be used to retrieve model coefficients between the values output by lars_path

Examples

Comparing lasso_path and lars_path with interpolation:

>>> X = np.array([[1, 2, 3.1], [2.3, 5.4, 4.3]]).T
>>> y = np.array([1, 2, 3.1])
>>> # Use lasso_path to compute a coefficient path
>>> _, coef_path, _ = lasso_path(X, y, alphas=[5., 1., .5])
>>> print(coef_path)
[[0.         0.         0.46874778]
 [0.2159048  0.4425765  0.23689075]]

>>> # Now use lars_path and 1D linear interpolation to compute the
>>> # same path
>>> from sklearn.linear_model import lars_path
>>> alphas, active, coef_path_lars = lars_path(X, y, method='lasso')
>>> from scipy import interpolate
>>> coef_path_continuous = interpolate.interp1d(alphas[::-1],
...                                             coef_path_lars[:, ::-1])
>>> print(coef_path_continuous([5., 1., .5]))
[[0.         0.         0.46915237]
 [0.2159048  0.4425765  0.23668876]]

predict(self, 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(self, 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

Xarray-like, 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.
yarray-like, shape = (n_samples) or (n_samples, n_outputs): True values for X.
sample_weightarray-like, shape = [n_samples], optional: Sample weights.

Returns

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

Notes

The R2 score used when calling score on a regressor will use multioutput='uniform_average' from version 0.23 to keep consistent with r2_score. This will influence the score method of all the multioutput regressors (except for MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call r2_score directly or make a custom scorer with make_scorer (the built-in scorer 'r2' uses multioutput='uniform_average').

set_params(self, **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.

Returns

self

3.2.4.1.7. sklearn.linear_model.MultiTaskLassoCV¶

3.2.4.1.7. `sklearn.linear_model`.MultiTaskLassoCV¶