3.2.4.1.3. 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, n_jobs=1, positive=False, random_state=None, selection='cyclic')[source]¶
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
Read more in the User Guide.
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 : int, cross-validation generator or an iterable, optional
Determines the cross-validation splitting strategy. Possible inputs for cv are:
- None, to use the default 3-fold cross-validation,
- integer, to specify the number of folds.
- An object to be used as a cross-validation generator.
- An iterable yielding train/test splits.
For integer/None inputs, KFold is used.
Refer User Guide for the various cross-validation strategies that can be used here.
verbose : bool or integer
Amount of verbosity.
n_jobs : integer, optional
Number of CPUs to use during the cross validation. If -1, use all the CPUs.
positive : bool, optional
If positive, restrict regression coefficients to be positive
selection : str, default ‘cyclic’
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.
random_state : int, RandomState instance, or None (default)
The seed of the pseudo random number generator that selects a random feature to update. Useful only when selection is set to ‘random’.
fit_intercept : boolean, default True
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).
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.
Attributes: alpha_ : float
The amount of penalization chosen by cross validation
coef_ : array, shape (n_features,) | (n_targets, n_features)
parameter vector (w in the cost function formula)
intercept_ : float | array, shape (n_targets,)
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, shape (n_alphas,)
The grid of alphas used for fitting
dual_gap_ : ndarray, shape ()
The dual gap at the end of the optimization for the optimal alpha (alpha_).
n_iter_ : int
number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.
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.
Methods
decision_function(*args, **kwargs) DEPRECATED: and will be removed in 0.19. fit(X, y) Fit linear model with coordinate descent get_params([deep]) Get parameters for this estimator. path(X, y[, eps, n_alphas, alphas, ...]) Compute Lasso path with coordinate descent predict(X) Predict using the linear model score(X, y[, sample_weight]) Returns the coefficient of determination R^2 of the prediction. set_params(**params) Set the parameters of this 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, n_jobs=1, positive=False, random_state=None, selection='cyclic')[source]¶
- decision_function(*args, **kwargs)[source]¶
DEPRECATED: and will be removed in 0.19.
Decision function of the linear model.
Parameters: X : {array-like, sparse matrix}, shape = (n_samples, n_features)
Samples.
Returns: C : array, shape = (n_samples,)
Returns predicted values.
- fit(X, y)[source]¶
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 float64, Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output, X can be sparse.
y : array-like, shape (n_samples,) or (n_samples, n_targets)
Target values
- get_params(deep=True)[source]¶
Get parameters for this estimator.
Parameters: deep: boolean, optional :
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns: params : mapping of string to any
Parameter names mapped to their values.
- static path(X, y, eps=0.001, n_alphas=100, alphas=None, precompute='auto', Xy=None, copy_X=True, coef_init=None, verbose=False, return_n_iter=False, positive=False, **params)[source]¶
Compute Lasso path with coordinate descent
The Lasso optimization function varies for mono and multi-outputs.
For mono-output tasks it is:
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
For multi-output tasks it is:
(1 / (2 * n_samples)) * ||Y - XW||^2_Fro + alpha * ||W||_21
Where:
||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}i.e. the sum of norm of each row.
Read more in the User Guide.
Parameters: X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output then X can be sparse.
y : ndarray, shape (n_samples,), or (n_samples, n_outputs)
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.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
coef_init : array, shape (n_features, ) | None
The initial values of the coefficients.
verbose : bool or integer
Amount of verbosity.
params : kwargs
keyword arguments passed to the coordinate descent solver.
positive : bool, default False
If set to True, forces coefficients to be positive.
return_n_iter : bool
whether to return the number of iterations or not.
Returns: alphas : array, shape (n_alphas,)
The alphas along the path where models are computed.
coefs : array, shape (n_features, n_alphas) or (n_outputs, n_features, n_alphas)
Coefficients along the path.
dual_gaps : array, shape (n_alphas,)
The dual gaps at the end of the optimization for each alpha.
n_iters : array-like, shape (n_alphas,)
The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha.
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 coefficients 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, _ = lasso_path(X, y, alphas=[5., 1., .5]) >>> print(coef_path) [[ 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)[source]¶
Predict using the linear model
Parameters: X : {array-like, sparse matrix}, shape = (n_samples, n_features)
Samples.
Returns: C : array, shape = (n_samples,)
Returns predicted values.
- score(X, y, sample_weight=None)[source]¶
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 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.
Parameters: X : array-like, shape = (n_samples, n_features)
Test samples.
y : array-like, shape = (n_samples) or (n_samples, n_outputs)
True values for X.
sample_weight : array-like, shape = [n_samples], optional
Sample weights.
Returns: score : float
R^2 of self.predict(X) wrt. y.
- set_params(**params)[source]¶
Set the parameters of this 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 :
