8.17.8. 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 cost function 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 alphas_: numpy array The grid of alphas used for fitting Methods
decision_function(X) Decision function of the linear model fit(X, y) Fit linear model with coordinate descent 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
Fit is on grid of alphas and best alpha estimated by cross-validation.
Parameters: X : array-like, shape (n_samples, n_features)
Training data. Pass directly as fortran contiguous data to avoid unnecessary memory duplication
y : narray, shape (n_samples,) or (n_samples, n_targets)
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 : ndarray, shape = (n_samples, n_features)
Training data. Pass directly as fortran contiguous data to avoid unnecessary memory duplication
y : ndarray, 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 : ndarray, 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, 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.
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.
Note that in certain cases, the Lars solver may be significantly faster to implement this functionality. In particular, linear interpolation can be used to retrieve model coefficents between the values output by lars_path
Examples
Comparing lasso_path and lars_path with interpolation:
>>> X = np.array([[1, 2, 3.1], [2.3, 5.4, 4.3]]).T >>> y = np.array([1, 2, 3.1]) >>> # Use lasso_path to compute a coefficient path >>> coef_path = [e.coef_ for e in lasso_path(X, y, alphas=[5., 1., .5], fit_intercept=False)] >>> print np.array(coef_path).T [[ 0. 0. 0.46874778] [ 0.2159048 0.4425765 0.23689075]]
>>> # Now use lars_path and 1D linear interpolation to compute the >>> # same path >>> from sklearn.linear_model import lars_path >>> alphas, active, coef_path_lars = lars_path(X, y, method='lasso') >>> from scipy import interpolate >>> coef_path_continuous = interpolate.interp1d(alphas[::-1], coef_path_lars[:, ::-1]) >>> print coef_path_continuous([5., 1., .5]) [[ 0. 0. 0.46915237] [ 0.2159048 0.4425765 0.23668876]]
- 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 :