8.15.1.6. sklearn.linear_model.LassoCV¶
- class sklearn.linear_model.LassoCV(eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, precompute='auto', max_iter=1000, tol=0.0001, copy_X=True, cv=None, verbose=False)¶
Lasso linear model with iterative fitting along a regularization path
The best model is selected by cross-validation.
The optimization objective for Lasso is:
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
Parameters : eps : float, optional
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.
n_alphas : int, optional
Number of alphas along the regularization path
alphas : numpy array, optional
List of alphas where to compute the models. If None alphas are set automatically
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.
cv : integer or crossvalidation generator, optional
If an integer is passed, it is the number of fold (default 3). Specific crossvalidation objects can be passed, see sklearn.cross_validation module for the list of possible objects
verbose : bool or integer
amount of verbosity
See also
Notes
See examples/linear_model/lasso_path_with_crossvalidation.py for an example.
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a fortran contiguous numpy array.
Attributes
alpha_: float The amount of penalization choosen by cross validation coef_ array, shape = [n_features] parameter vector (w in the fomulation formula) intercept_ float independent term in decision function. mse_path_: array, shape = [n_alphas, n_folds] mean square error for the test set on each fold, varying alpha Methods
decision_function(X) Decision function of the linear model fit(X, y) Fit linear model with coordinate descent along decreasing alphas get_params([deep]) Get parameters for the estimator path(X, y[, eps, n_alphas, alphas, ...]) Compute Lasso path 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__(eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, precompute='auto', max_iter=1000, tol=0.0001, copy_X=True, cv=None, verbose=False)¶
- 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)¶
Fit linear model with coordinate descent along decreasing alphas using cross-validation
Parameters : X : numpy array of shape [n_samples,n_features]
Training data. Pass directly as fortran contiguous data to avoid unnecessary memory duplication
y : numpy array of shape [n_samples]
Target values
- 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.
- static path(X, y, eps=0.001, n_alphas=100, alphas=None, precompute='auto', Xy=None, fit_intercept=True, normalize=False, copy_X=True, verbose=False, **params)¶
Compute Lasso path with coordinate descent
The optimization objective for Lasso is:
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
Parameters : X : numpy array of shape [n_samples,n_features]
Training data. Pass directly as fortran contiguous data to avoid unnecessary memory duplication
y : numpy array of shape [n_samples]
Target values
eps : float, optional
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3
n_alphas : int, optional
Number of alphas along the regularization path
alphas : numpy array, optional
List of alphas where to compute the models. If None alphas are set automatically
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 precomputed.
fit_intercept : bool
Fit or not an intercept
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.
verbose : bool or integer
Amount of verbosity
params : kwargs
keyword arguments passed to the Lasso objects
Returns : models : a list of models along the regularization path
See also
lars_path, Lasso, LassoLars, LassoCV, LassoLarsCV, sklearn.decomposition.sparse_encode
Notes
See examples/linear_model/plot_lasso_coordinate_descent_path.py for an example.
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a fortran contiguous numpy array.
- 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 :