MultiTaskLasso

class sklearn.linear_model.MultiTaskLasso(alpha=1.0, *, fit_intercept=True, copy_X=True, max_iter=1000, tol=0.0001, warm_start=False, random_state=None, selection='cyclic')

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

The optimization objective for Lasso 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.

Read more in the User Guide.

Parameters:

alphafloat, default=1.0

Constant that multiplies the L1/L2 term. Defaults to 1.0.

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).

copy_Xbool, default=True

If True, X will be copied; else, it may be overwritten.

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.

warm_startbool, default=False

When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.

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:

coef_ndarray of shape (n_targets, n_features)

Parameter vector (W in the cost function formula). Note that coef_ stores the transpose of W, W.T.

intercept_ndarray of shape (n_targets,)

Independent term in decision function.

n_iter_int

Number of iterations run by the coordinate descent solver to reach the specified tolerance.

dual_gap_ndarray of shape (n_alphas,)

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

eps_float

The tolerance scaled scaled by the variance of the target y.

sparse_coef_sparse matrix of shape (n_features,) or (n_targets, n_features)

Sparse representation of the fitted coef_.

n_features_in_int

Number of features seen during fit.

Added in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

Added in version 1.0.

See also

Lasso

Linear Model trained with L1 prior as regularizer (aka the Lasso).

MultiTaskLassoCV

Multi-task L1 regularized linear model with built-in cross-validation.

MultiTaskElasticNetCV

Multi-task L1/L2 ElasticNet with built-in cross-validation.

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.MultiTaskLasso(alpha=0.1)
>>> clf.fit([[0, 1], [1, 2], [2, 4]], [[0, 0], [1, 1], [2, 3]])
MultiTaskLasso(alpha=0.1)
>>> print(clf.coef_)
[[0.         0.60809415]
[0.         0.94592424]]
>>> print(clf.intercept_)
[-0.41888636 -0.87382323]

fit(X, y)

Fit MultiTaskElasticNet model with coordinate descent.

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

Fitted estimator.

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_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)

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, *, l1_ratio=0.5, 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, check_input=True, **params)

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_targets)

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.

alphasarray-like, 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_targets), 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_initarray-like 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_targets, 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

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

MultiTaskElasticNetCV

Multi-task L1/L2 ElasticNet with built-in cross-validation.

ElasticNet

Linear regression with combined L1 and L2 priors as regularizer.

ElasticNetCV

Elastic Net model with iterative fitting along a regularization path.

Notes

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

Examples

>>> from sklearn.linear_model import enet_path
>>> from sklearn.datasets import make_regression
>>> X, y, true_coef = make_regression(
...    n_samples=100, n_features=5, n_informative=2, coef=True, random_state=0
... )
>>> true_coef
array([ 0.        ,  0.        ,  0.        , 97.9..., 45.7...])
>>> alphas, estimated_coef, _ = enet_path(X, y, n_alphas=3)
>>> alphas.shape
(3,)
>>> estimated_coef
 array([[ 0.        ,  0.78...,  0.56...],
        [ 0.        ,  1.12...,  0.61...],
        [-0.        , -2.12..., -1.12...],
        [ 0.        , 23.04..., 88.93...],
        [ 0.        , 10.63..., 41.56...]])

predict(X)

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)

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) w.r.t. 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_fit_request(*, check_input: bool | None | str = '$UNCHANGED$', sample_weight: bool | None | str = '$UNCHANGED$') → MultiTaskLasso

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to fit.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

check_inputstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for check_input parameter in fit.

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for sample_weight parameter in fit.

Returns:

selfobject

The updated object.

set_params(**params)

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.

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → MultiTaskLasso

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to score.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for sample_weight parameter in score.

Returns:

selfobject

The updated object.

property sparse_coef_

Sparse representation of the fitted coef_.

Gallery examples

Joint feature selection with multi-task Lasso

Joint feature selection with multi-task Lasso