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class sklearn.linear_model.MultiTaskElasticNetCV(l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, max_iter=1000, tol=0.0001, cv=None, copy_X=True, verbose=0, n_jobs=1, random_state=None, selection='cyclic')
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Multi-task L1/L2 ElasticNet with built-in cross-validation.
The optimization objective for MultiTaskElasticNet 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: eps : float, optional
Length of the path.
eps=1e-3
means thatalpha_min / alpha_max = 1e-3
.alphas : array-like, optional
List of alphas where to compute the models. If not provided, set automatically.
n_alphas : int, optional
Number of alphas along the regularization path
l1_ratio : float or array of floats
The ElasticNet mixing parameter, with 0 < l1_ratio <= 1. For l1_ratio = 0 the penalty is an L1/L2 penalty. For l1_ratio = 1 it is an L1 penalty. For
0 < l1_ratio < 1
, the penalty is a combination of L1/L2 and L2. This parameter can be a list, in which case the different values are tested by cross-validation and the one giving the best prediction score is used. Note that a good choice of list of values for l1_ratio is often to put more values close to 1 (i.e. Lasso) and less close to 0 (i.e. Ridge), as in[.1, .5, .7, .9, .95, .99, 1]
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).
normalize : boolean, optional, default False
If
True
, the regressors X will be normalized before regression. This parameter is ignored whenfit_intercept
is set toFalse
. When the regressors are normalized, note that this makes the hyperparameters learnt more robust and almost independent of the number of samples. The same property is not valid for standardized data. However, if you wish to standardize, please usepreprocessing.StandardScaler
before callingfit
on an estimator withnormalize=False
.copy_X : boolean, optional, default True
If
True
, X will be copied; else, it may be overwritten.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 thantol
.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. Note that this is used only if multiple values for l1_ratio are given.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?.
Attributes: intercept_ : array, shape (n_tasks,)
Independent term in decision function.
coef_ : array, shape (n_tasks, n_features)
Parameter vector (W in the cost function formula).
alpha_ : float
The amount of penalization chosen by cross validation
mse_path_ : array, shape (n_alphas, n_folds) or (n_l1_ratio, n_alphas, n_folds)
mean square error for the test set on each fold, varying alpha
alphas_ : numpy array, shape (n_alphas,) or (n_l1_ratio, n_alphas)
The grid of alphas used for fitting, for each l1_ratio
l1_ratio_ : float
best l1_ratio obtained by cross-validation.
n_iter_ : int
number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.
See also
Notes
The algorithm used to fit the model is coordinate descent.
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.
Examples
>>> from sklearn import linear_model >>> clf = linear_model.MultiTaskElasticNetCV() >>> clf.fit([[0,0], [1, 1], [2, 2]], ... [[0, 0], [1, 1], [2, 2]]) ... MultiTaskElasticNetCV(alphas=None, copy_X=True, cv=None, eps=0.001, fit_intercept=True, l1_ratio=0.5, max_iter=1000, n_alphas=100, n_jobs=1, normalize=False, random_state=None, selection='cyclic', tol=0.0001, verbose=0) >>> print(clf.coef_) [[ 0.52875032 0.46958558] [ 0.52875032 0.46958558]] >>> print(clf.intercept_) [ 0.00166409 0.00166409]
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[, l1_ratio, eps, n_alphas, ...])Compute elastic net 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__(l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, max_iter=1000, tol=0.0001, cv=None, copy_X=True, verbose=0, n_jobs=1, random_state=None, selection='cyclic')
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decision_function(*args, **kwargs)
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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.
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fit(X, y)
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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
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get_params(deep=True)
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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.
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static 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)
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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: 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 thenX
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 Lassoeps : float
Length of the path.
eps=1e-3
means thatalpha_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.
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.
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.
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. (Is returned when
return_n_iter
is set to True).Notes
See examples/linear_model/plot_lasso_coordinate_descent_path.py for an example.
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predict(X)
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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.
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score(X, y, sample_weight=None)
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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.
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set_params(**params)
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Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form
<component>__<parameter>
so that it?s possible to update each component of a nested object.Returns: self :
linear_model.MultiTaskElasticNetCV()
2017-01-15 04:23:33
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