8.17.9. sklearn.linear_model.LassoLars¶

class sklearn.linear_model.LassoLars(alpha=1.0, fit_intercept=True, verbose=False, normalize=True, precompute='auto', max_iter=500, eps=2.2204460492503131e-16, copy_X=True, fit_path=True)¶

Lasso model fit with Least Angle Regression a.k.a. Lars

It is a Linear Model trained with an L1 prior as regularizer.

The optimization objective for Lasso is:

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

Parameters:

alpha : float

Constant that multiplies the penalty 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 with the LassoLars 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).

verbose : boolean or integer, optional

Sets the verbosity amount

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.

max_iter: integer, optional :

Maximum number of iterations to perform.

eps: float, optional :

The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the ‘tol’ parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.

fit_path : boolean

If True the full path is stored in the coef_path_ attribute. If you compute the solution for a large problem or many targets, setting fit_path to False will lead to a speedup, especially with a small alpha.

http: //en.wikipedia.org/wiki/Least_angle_regression

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.LassoLars(alpha=0.01)
>>> clf.fit([[-1, 1], [0, 0], [1, 1]], [-1, 0, -1])
... 
LassoLars(alpha=0.01, copy_X=True, eps=..., fit_intercept=True,
     fit_path=True, max_iter=500, normalize=True, precompute='auto',
     verbose=False)
>>> print(clf.coef_) 
[ 0.         -0.963257...]

Attributes

coef_path_	array, shape = [n_features, n_alpha]	The varying values of the coefficients along the path. It is not present if fit_path parameter is False.
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])	Fit the model using X, y as training data.
`get_params`([deep])	Get parameters for the estimator
`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, verbose=False, normalize=True, precompute='auto', max_iter=500, eps=2.2204460492503131e-16, copy_X=True, fit_path=True)¶

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)¶

Fit the model using X, y as training data.

Parameters:

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

Training data.

y : array-like, shape = [n_samples] or [n_samples, n_targets]

Target values.

Xy : array-like, shape = [n_samples] or [n_samples, n_targets], optional

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

Returns:

self : object

returns an instance of self.

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 :

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8.17.9. sklearn.linear_model.LassoLars¶