`sklearn.linear_model`.MultiTaskLassoCV¶

class sklearn.linear_model.MultiTaskLassoCV(*, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize='deprecated', 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: Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer.
ElasticNetCV: Elastic net model with best model selection by cross-validation.
MultiTaskElasticNetCV: Multi-task L1/L2 ElasticNet with built-in cross-validation.

Notes

The algorithm used to fit the model is coordinate descent.

In fit, once the best parameter alpha is found through cross-validation, the model is fit again using the entire training set.

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.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`(X, y)	Fit MultiTaskLasso model with coordinate descent.
`get_params`([deep])	Get parameters for this estimator.
`path`(X, y, *[, eps, n_alphas, alphas, ...])	Compute Lasso path with coordinate descent.
`predict`(X)	Predict using the linear model.
`score`(X, y[, sample_weight])	Return the coefficient of determination of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

fit(X, y)[source]¶

Fit MultiTaskLasso model with coordinate descent.

Fit is on grid of alphas and best alpha estimated by cross-validation.

Parameters:

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

Returns:

selfobject: Returns an instance of fitted model.

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(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: Compute Least Angle Regression or Lasso path using LARS algorithm.
Lasso: The Lasso is a linear model that estimates sparse coefficients.
LassoLars: Lasso model fit with Least Angle Regression a.k.a. Lars.
LassoCV: Lasso linear model with iterative fitting along a regularization path.
LassoLarsCV: Cross-validated Lasso using the LARS algorithm.
sklearn.decomposition.sparse_encode: Estimator that can be used to transform signals into sparse linear combination of atoms from a fixed.

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:

>>> import numpy as np
>>> from sklearn.linear_model import lasso_path
>>> 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(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 of the prediction.

The coefficient of determination \(R^2\) 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.

sklearn.linear_model.MultiTaskLassoCV¶

`sklearn.linear_model`.MultiTaskLassoCV¶