econml.sklearn_extensions.linear_model.WeightedLassoCV

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

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

Version of sklearn LassoCV 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 (numpy array, optional) – List of alphas where to compute the models. If None alphas are set automatically

• 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).

• 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.

• copy_X (boolean, optional, default True) – If True, X will be copied; else, it may be overwritten.

• cv (int, cross-validation generator or an iterable, optional (default=None)) – 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 integer) – Amount of verbosity.

• n_jobs (int or None, optional (default=None)) – Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

• positive (bool, optional) – If positive, restrict regression coefficients to be positive

• 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.

__init__(eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, precompute='auto', max_iter=1000, tol=0.0001, normalize=False, copy_X=True, cv=None, verbose=False, n_jobs=None, positive=False, 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 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.

(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1


(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} of 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 ({array-like, sparse matrix} of shape (n_samples,) or (n_samples, n_targets)) – Target values.

• eps (float, default=1e-3) – Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.

• n_alphas (int, default=100) – Number of alphas along the regularization path.

• alphas (ndarray, default=None) – List of alphas where to compute the models. If None alphas are set automatically.

• precompute (‘auto’, bool or array-like of shape (n_features, n_features), default=’auto’) – 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 of shape (n_features,) or (n_features, n_targets), default=None) – Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.

• copy_X (bool, default=True) – If True, X will be copied; else, it may be overwritten.

• coef_init (ndarray of shape (n_features, ), default=None) – The initial values of the coefficients.

• verbose (bool or int, default=False) – Amount of verbosity.

• return_n_iter (bool, default=False) – 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).

• **params (kwargs) – Keyword arguments passed to the coordinate descent solver.

Returns

• alphas (ndarray of shape (n_alphas,)) – The alphas along the path where models are computed.

• coefs (ndarray of shape (n_features, n_alphas) or (n_targets, n_features, n_alphas)) – Coefficients along the path.

• dual_gaps (ndarray of shape (n_alphas,)) – The dual gaps at the end of the optimization for each alpha.

• n_iters (list of int) – The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha.

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) wrt. 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