8.14.1.12. sklearn.linear_model.LassoLarsIC

class sklearn.linear_model.LassoLarsIC(criterion='aic', fit_intercept=True, verbose=False, normalize=True, precompute='auto', max_iter=500, eps=2.2204460492503131e-16, copy_X=True)

Lasso model fit with Lars using BIC or AIC for model selection

The optimization objective for Lasso is:

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

AIC is the Akaike information criterion and BIC is the Bayes Information criterion. Such criteria are useful to select the value of the regularization parameter by making a trade-off between the goodness of fit and the complexity of the model. A good model should explain well the data while being simple.

Parameters :

criterion: ‘bic’ | ‘aic’ :

The type of criterion to use.

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

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: integer, optional :

Maximum number of iterations to perform. Can be used for early stopping.

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.

See also

lars_path, LassoLars, LassoLarsCV

Notes

The estimation of the number of degrees of freedom is given by:

“On the degrees of freedom of the lasso” Hui Zou, Trevor Hastie, and Robert Tibshirani Ann. Statist. Volume 35, Number 5 (2007), 2173-2192.

http://en.wikipedia.org/wiki/Akaike_information_criterion http://en.wikipedia.org/wiki/Bayesian_information_criterion

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.LassoLarsIC(criterion='bic')
>>> clf.fit([[-1, 1], [0, 0], [1, 1]], [-1.1111, 0, -1.1111])
... 
LassoLarsIC(copy_X=True, criterion='bic', eps=..., fit_intercept=True,
      max_iter=500, normalize=True, precompute='auto',
      verbose=False)
>>> print clf.coef_ 
[ 0.  -1.11...]

Attributes

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

Methods

decision_function(X)	Decision function of the linear model
fit(X, y[, copy_X])	Fit the model using X, y as training data.
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__(criterion='aic', fit_intercept=True, verbose=False, normalize=True, precompute='auto', max_iter=500, eps=2.2204460492503131e-16, copy_X=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, copy_X=True)

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]

target values.

Returns :

self : object

returns an instance of self.

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 :