sklearn.linear_model.enet_path
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sklearn.linear_model.enet_path(X, y, l1_ratio=0.5, 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, check_input=True, **params)
[source]
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Compute elastic net path with coordinate descent
The elastic net optimization function varies for mono and multi-outputs.
For mono-output tasks it is:
1 / (2 * n_samples) * ||y - Xw||^2_2
+ alpha * l1_ratio * ||w||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2
For multi-output tasks it is:
(1 / (2 * n_samples)) * ||Y - XW||^Fro_2
+ alpha * l1_ratio * ||W||_21
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2
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: |
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X : {array-like}, 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 -
l1_ratio : float, optional -
float between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). l1_ratio=1 corresponds to the Lasso -
eps : float -
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. -
return_n_iter : bool -
whether to return the number of iterations or not. -
positive : bool, default False -
If set to True, forces coefficients to be positive. (Only allowed when y.ndim == 1 ). -
check_input : bool, default True -
Skip input validation checks, including the Gram matrix when provided assuming there are handled by the caller when check_input=False. -
**params : kwargs -
keyword arguments passed to the coordinate descent solver. |
Returns: |
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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. (Is returned when return_n_iter is set to True). |
Notes
For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.
Examples using sklearn.linear_model.enet_path