6.2.3. scikits.learn.linear_model.Lasso

class scikits.learn.linear_model.Lasso(alpha=1.0, fit_intercept=True)

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

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).

See also

LassoLARS

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 scikits.learn 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, fit_intercept=True)
>>> 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

fit(X, y[, precompute, Xy, max_iter, tol, ...])	Fit Elastic Net model with coordinate descent
predict(X)	Predict using the linear model
score(X, y)	Returns the coefficient of determination of the prediction

__init__(alpha=1.0, fit_intercept=True)

fit(X, y, precompute='auto', Xy=None, max_iter=1000, tol=0.0001, coef_init=None, **params)

Fit Elastic Net model with coordinate descent

Parameters :

X: ndarray, (n_samples, n_features) :

Data

y: ndarray, (n_samples) :

Target

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 precomuted.

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.

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 of the prediction

Parameters :

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

Training set.

y : array-like, shape = [n_samples]

Returns :

z : float