8.14.1.4. sklearn.linear_model.Lasso

class sklearn.linear_model.Lasso(alpha=1.0, fit_intercept=True, normalize=False, precompute='auto', copy_X=True, max_iter=1000, tol=0.0001)

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

The optimization objective for Lasso is:

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

Technically the Lasso model is optimizing the same objective function as the Elastic Net with rho=1.0 (no L2 penalty).

Parameters :

alpha : float, optional

Constant that multiplies the L1 term. Defaults to 1.0

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

If True, the regressors X are normalized

copy_X : boolean, optional, default True

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

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.

See also

lars_path, lasso_path, LassoLars, LassoCV, LassoLarsCV, sklearn.decomposition.sparse_encode

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 import linear_model
>>> clf = linear_model.Lasso(alpha=0.1)
>>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
Lasso(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=1000,
   normalize=False, precompute='auto', tol=0.0001)
>>> print clf.coef_
[ 0.85  0.  ]
>>> print clf.intercept_
0.15

Attributes

coef_	array, shape = [n_features]	parameter vector (w in the fomulation formula)
intercept_	float	independent term in decision function.

Methods

decision_function(X)	Decision function of the linear model
fit(X, y[, Xy, coef_init])	Fit Elastic Net model with coordinate descent
predict(X)	Predict using the linear model
score(X, y)	Returns the coefficient of determination R^2 of the prediction.
set_params(**params)	Set the parameters of the estimator.

__init__(alpha=1.0, fit_intercept=True, normalize=False, precompute='auto', copy_X=True, max_iter=1000, tol=0.0001)

decision_function(X)

Decision function of the linear model

Parameters :

X : numpy array of shape [n_samples, n_features]

Returns :

C : array, shape = [n_samples]

Returns predicted values.

fit(X, y, Xy=None, coef_init=None)

Fit Elastic Net model with coordinate descent

Parameters :

X: ndarray, (n_samples, n_features) :

Data

y: ndarray, (n_samples) :

Target

Xy : array-like, optional

Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.

coef_init: ndarray of shape n_features :

The initial coeffients to warm-start the optimization

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.

predict(X)

Predict using the linear model

Parameters :

X : numpy array of shape [n_samples, n_features]

Returns :

C : array, shape = [n_samples]

Returns predicted values.

score(X, y)

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 - 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, lower values are worse.

Parameters :

X : array-like, shape = [n_samples, n_features]

Training set.

y : array-like, shape = [n_samples]

Returns :

z : float

set_params(**params)

Set the parameters of the estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns :self :