8.17.7. 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, warm_start=False, positive=False)

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 l1_ratio=1.0 (no L2 penalty).

Parameters :

alpha : float, optional

Constant that multiplies the L1 term. Defaults to 1.0 alpha = 0 is equivalent to an ordinary least square, solved by the LinearRegression object in the scikit. For numerical reasons, using alpha = 0 is with the Lasso object is not advised and you should prefer the LinearRegression object.

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, default False

If True, the regressors X will be normalized before regression.

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. For sparse input this option is always True to preserve sparsity.

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.

warm_start : bool, optional

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

positive : bool, optional

When set to True, forces the coefficients to be positive.

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, positive=False, precompute='auto', tol=0.0001,
   warm_start=False)
>>> print(clf.coef_)
[ 0.85  0.  ]
>>> print(clf.intercept_)
0.15

Attributes

coef_ array, shape = (n_features,) parameter vector (w in the cost function formula)
sparse_coef_ scipy.sparse matrix, shape = (n_features, 1) sparse_coef_ is a readonly property derived from coef_
intercept_ float independent term in decision function.
dual_gap_ float the current fit is guaranteed to be epsilon-suboptimal with epsilon := dual_gap_
eps_ float eps_ is used to check if the fit converged to the requested tol

Methods

decision_function
fit
get_params
predict
score
set_params
__init__(alpha=1.0, fit_intercept=True, normalize=False, precompute='auto', copy_X=True, max_iter=1000, tol=0.0001, warm_start=False, positive=False)
decision_function(X)

Decision function of the linear model

Parameters :

X : numpy array or scipy.sparse matrix of shape (n_samples, n_features)

Returns :

T : array, shape = (n_samples,)

The predicted decision function

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

Fit model with coordinate descent

Parameters :

X: ndarray or scipy.sparse matrix, (n_samples, n_features) :

Data

y: ndarray, shape = (n_samples,) or (n_samples, n_targets) :

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 or (n_targets, 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.

get_params(deep=True)

Get parameters for the estimator

Parameters :

deep: boolean, optional :

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

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_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, 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 :
sparse_coef_

sparse representation of the fitted coef

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