linear_model.LassoCV()

class sklearn.linear_model.LassoCV(eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, precompute='auto', max_iter=1000, tol=0.0001, copy_X=True, cv=None, verbose=False, n_jobs=1, positive=False, random_state=None, selection='cyclic') [source]

Lasso linear model with iterative fitting along a regularization path

The best model is selected by cross-validation.

The optimization objective for Lasso is:

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

Parameters:	eps : float, optional Length of the path. `eps=1e-3` means that `alpha_min / alpha_max = 1e-3`. n_alphas : int, optional Number of alphas along the regularization path alphas : numpy array, optional List of alphas where to compute the models. If `None` alphas are set automatically precompute : True \| False \| ?auto? \| array-like 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. 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`. cv : int, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy. Possible inputs for cv are: None, to use the default 3-fold cross-validation, integer, to specify the number of folds. An object to be used as a cross-validation generator. An iterable yielding train/test splits. For integer/None inputs, `KFold` is used. Refer User Guide for the various cross-validation strategies that can be used here. verbose : bool or integer Amount of verbosity. n_jobs : integer, optional Number of CPUs to use during the cross validation. If `-1`, use all the CPUs. positive : bool, optional If positive, restrict regression coefficients to be positive 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. random_state : int, RandomState instance, or None (default) The seed of the pseudo random number generator that selects a random feature to update. Useful only when selection is set to ?random?. fit_intercept : boolean, default True 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 If `True`, the regressors X will be normalized before regression. This parameter is ignored when `fit_intercept` is set to `False`. When the regressors are normalized, note that this makes the hyperparameters learnt more robust and almost independent of the number of samples. The same property is not valid for standardized data. However, if you wish to standardize, please use `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.
Attributes:	alpha_ : float The amount of penalization chosen by cross validation coef_ : array, shape (n_features,) \| (n_targets, n_features) parameter vector (w in the cost function formula) intercept_ : float \| array, shape (n_targets,) independent term in decision function. mse_path_ : array, shape (n_alphas, n_folds) mean square error for the test set on each fold, varying alpha alphas_ : numpy array, shape (n_alphas,) The grid of alphas used for fitting dual_gap_ : ndarray, shape () The dual gap at the end of the optimization for the optimal alpha (`alpha_`). n_iter_ : int number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.

Notes

See examples/linear_model/plot_lasso_model_selection.py for an example.

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

Methods

`decision_function`(\args, \\*kwargs)	DEPRECATED: and will be removed in 0.19.
`fit`(X, y)	Fit linear 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])	Returns the coefficient of determination R^2 of the prediction.
`set_params`(\\params)	Set the parameters of this estimator.

__init__(eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, precompute='auto', max_iter=1000, tol=0.0001, copy_X=True, cv=None, verbose=False, n_jobs=1, positive=False, random_state=None, selection='cyclic') [source]

decision_function(*args, **kwargs) [source]

DEPRECATED: and will be removed in 0.19.

Decision function of the linear model.

Parameters:

Parameters:	X : {array-like, sparse matrix}, shape = (n_samples, n_features) Samples.
Returns:	C : array, shape = (n_samples,) Returns predicted values.

X : {array-like, sparse matrix}, shape = (n_samples, n_features)

Samples.

Returns:

C : array, shape = (n_samples,)

Returns predicted values.

fit(X, y) [source]

Fit linear model with coordinate descent

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

Parameters:

Parameters:	X : {array-like}, shape (n_samples, n_features) Training data. Pass directly as float64, Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output, X can be sparse. y : array-like, shape (n_samples,) or (n_samples, n_targets) Target values

X : {array-like}, shape (n_samples, n_features)

Training data. Pass directly as float64, Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output, X can be sparse.

y : array-like, shape (n_samples,) or (n_samples, n_targets)

Target values

get_params(deep=True) [source]

Get parameters for this estimator.

Parameters:

Parameters:	deep : boolean, optional If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:	params : mapping of string to any Parameter names mapped to their values.

deep : boolean, optional

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

Returns:

params : mapping 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.

Parameters:	X : {array-like, sparse matrix}, 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 : ndarray, shape (n_samples,), or (n_samples, n_outputs) Target values eps : float, optional Length of the path. `eps=1e-3` means that `alpha_min / alpha_max = 1e-3` n_alphas : int, optional Number of alphas along the regularization path alphas : ndarray, optional List of alphas where to compute the models. If `None` alphas are set automatically precompute : True \| False \| ?auto? \| array-like 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. Xy : array-like, optional Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed. copy_X : boolean, optional, default True If `True`, X will be copied; else, it may be overwritten. coef_init : array, shape (n_features, ) \| None The initial values of the coefficients. verbose : bool or integer Amount of verbosity. params : kwargs keyword arguments passed to the coordinate descent solver. positive : bool, default False If set to True, forces coefficients to be positive. return_n_iter : bool whether to return the number of iterations or not.
Returns:	alphas : array, shape (n_alphas,) The alphas along the path where models are computed. coefs : array, shape (n_features, n_alphas) or (n_outputs, n_features, n_alphas) Coefficients along the path. dual_gaps : array, shape (n_alphas,) The dual gaps at the end of the optimization for each alpha. n_iters : array-like, shape (n_alphas,) The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha.

Notes

See examples/linear_model/plot_lasso_coordinate_descent_path.py for an example.

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(X) [source]

Predict using the linear model

Parameters:

Parameters:	X : {array-like, sparse matrix}, shape = (n_samples, n_features) Samples.
Returns:	C : array, shape = (n_samples,) Returns predicted values.

X : {array-like, sparse matrix}, shape = (n_samples, n_features)

Samples.

Returns:

C : array, shape = (n_samples,)

Returns predicted values.

score(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 regression sum of squares ((y_true - y_pred) ** 2).sum() and v is the residual sum of squares ((y_true - y_true.mean()) ** 2).sum(). 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:

Parameters:	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.
Returns:	score : float R^2 of self.predict(X) wrt. y.

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.

Returns:

score : float

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

set_params(**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.