econml.sklearn_extensions.linear_model.WeightedMultiTaskLassoCV

class econml.sklearn_extensions.linear_model.WeightedMultiTaskLassoCV(eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, max_iter=1000, tol=0.0001, copy_X=True, cv=None, verbose=False, n_jobs=None, random_state=None, selection='cyclic')[source]

Bases: econml.sklearn_extensions.linear_model.WeightedModelMixin, sklearn.linear_model._coordinate_descent.MultiTaskLassoCV

Version of sklearn MultiTaskLassoCV that accepts weights.

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 (array_like, optional) – List of alphas where to compute the models. If not provided, set automatically.
fit_intercept (bool) – 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).
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.
copy_X (bool, default True) – If True, X will be copied; else, it may be overwritten.
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 weighted cross-validation, - integer, to specify the number of folds. - CV splitter, - An iterable yielding (train, test) splits as arrays of indices. For integer/None inputs, WeightedKFold is used.

If None then 5-folds are used.
verbose (bool or int) – Amount of verbosity.
n_jobs (int or None, optional) – Number of CPUs to use during the cross validation. Note that this is used only if multiple values for l1_ratio are given. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_state (int, RandomState instance, or None, 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.

__init__(eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, max_iter=1000, tol=0.0001, copy_X=True, cv=None, verbose=False, n_jobs=None, random_state=None, selection='cyclic')[source]

Methods

`__init__`([eps, n_alphas, alphas, ...])
`fit`(X, y[, sample_weight])	Fit 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])	Return the coefficient of determination of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

fit(X, y, sample_weight=None)[source]

Fit model with coordinate descent.

Parameters

X (ndarray or scipy.sparse matrix, (n_samples, n_features)) – Data
y (ndarray, shape (n_samples,) or (n_samples, n_targets)) – Target. Will be cast to X’s dtype if necessary
sample_weight (numpy array of shape [n_samples]) – Individual weights for each sample. The weights will be normalized internally.

get_params(deep=True)

Get parameters for this estimator.

Parameters: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns: params – Parameter names mapped to their values.
Return type: dict

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)

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.

See also

lars_path: Compute Least Angle Regression or Lasso path using LARS algorithm.
Lasso: The Lasso is a linear model that estimates sparse coefficients.
LassoLars: Lasso model fit with Least Angle Regression a.k.a. Lars.
LassoCV: Lasso linear model with iterative fitting along a regularization path.
LassoLarsCV: Cross-validated Lasso using the LARS algorithm.
sklearn.decomposition.sparse_encode: Estimator that can be used to transform signals into sparse linear combination of atoms from a fixed.

Notes

For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.

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:

>>> import numpy as np
>>> from sklearn.linear_model import lasso_path
>>> 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)

Predict using the linear model.

Parameters: X (array-like or sparse matrix, shape (n_samples, n_features)) – Samples.
Returns: C – Returns predicted values.
Return type: array, shape (n_samples,)

score(X, y, sample_weight=None)

Return the coefficient of determination of the prediction.

The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), 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.

Parameters

X (array-like of shape (n_samples, n_features)) – Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True values for X.
sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns

score – \(R^2\) of self.predict(X) w.r.t. y.

Return type

float

Notes

The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score(). This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters: **params (dict) – Estimator parameters.
Returns: self – Estimator instance.
Return type: estimator instance