MultiTaskElasticNetCV
¶
-
class
ibex.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')¶ Bases:
sklearn.linear_model.coordinate_descent.MultiTaskElasticNetCV
,ibex._base.FrameMixin
Note
The documentation following is of the class wrapped by this class. There are some changes, in particular:
- A parameter
X
denotes apandas.DataFrame
. - A parameter
y
denotes apandas.Series
.
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.
- l1_ratio : float or array of floats
- The ElasticNet mixing parameter, with 0 < l1_ratio <= 1.
For l1_ratio = 1 the penalty is an L1/L2 penalty. For l1_ratio = 0 it
is an L2 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]
- eps : float, optional
- 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 : array-like, optional
- List of alphas where to compute the models. If not provided, set automatically.
- 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
- This parameter is ignored when
fit_intercept
is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please usesklearn.preprocessing.StandardScaler
before callingfit
on an estimator withnormalize=False
. - 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.
- copy_X : boolean, optional, default True
- If
True
, X will be copied; else, it may be overwritten. - 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. - random_state : int, RandomState instance or None, optional, default None
- The seed of the pseudo random number generator that selects a random
feature to update. If int, random_state is the seed used by the random
number generator; If RandomState instance, random_state is the random
number generator; If None, the random number generator is the
RandomState instance used by np.random. Used when
selection
== ‘random’. - 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.
- 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).
Note that
coef_
stores the transpose ofW
,W.T
. - 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.
>>> 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]
MultiTaskElasticNet ElasticNetCV MultiTaskLassoCV
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.
-
fit
(X, y)¶ Note
The documentation following is of the class wrapped by this class. There are some changes, in particular:
- A parameter
X
denotes apandas.DataFrame
. - A parameter
y
denotes apandas.Series
.
Fit linear model with coordinate descent
Fit is on grid of alphas and best alpha estimated by cross-validation.
- 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, X can be sparse.
- y : array-like, shape (n_samples,) or (n_samples, n_targets)
- Target values
- A parameter
-
predict
(X)¶ Note
The documentation following is of the class wrapped by this class. There are some changes, in particular:
- A parameter
X
denotes apandas.DataFrame
. - A parameter
y
denotes apandas.Series
.
Predict using the linear model
- X : {array-like, sparse matrix}, shape = (n_samples, n_features)
- Samples.
- C : array, shape = (n_samples,)
- Returns predicted values.
- A parameter
-
score
(X, y, sample_weight=None)¶ Note
The documentation following is of the class wrapped by this class. There are some changes, in particular:
- A parameter
X
denotes apandas.DataFrame
. - A parameter
y
denotes apandas.Series
.
Returns the coefficient of determination R^2 of the prediction.
The coefficient R^2 is defined as (1 - u/v), where u is the residual sum of squares ((y_true - y_pred) ** 2).sum() and v is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The 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.
- 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.
- score : float
- R^2 of self.predict(X) wrt. y.
- A parameter
- A parameter