econml.sklearn_extensions.linear_model.DebiasedLasso

class econml.sklearn_extensions.linear_model.DebiasedLasso(alpha='auto', n_alphas=100, alpha_cov='auto', n_alphas_cov=10, fit_intercept=True, precompute=False, copy_X=True, max_iter=1000, tol=0.0001, warm_start=False, random_state=None, selection='cyclic', n_jobs=None)[source]

Bases: econml.sklearn_extensions.linear_model.WeightedLasso

Debiased Lasso model.

Implementation was derived from <https://arxiv.org/abs/1303.0518>.

Only implemented for single-dimensional output.

Parameters
  • alpha (string | float, optional, default ‘auto’.) – Constant that multiplies the L1 term. Defaults to ‘auto’. alpha = 0 is equivalent to an ordinary least square, solved by the LinearRegression object. For numerical reasons, using alpha = 0 with the Lasso object is not advised. Given this, you should use the LinearRegression object.

  • n_alphas (int, optional, default 100) – How many alphas to try if alpha=’auto’

  • alpha_cov (string | float, optional, default ‘auto’) – The regularization alpha that is used when constructing the pseudo inverse of the covariance matrix Theta used to for correcting the lasso coefficient. Each such regression corresponds to the regression of one feature on the remainder of the features.

  • n_alphas_cov (int, optional, default 10) – How many alpha_cov to try if alpha_cov=’auto’.

  • fit_intercept (boolean, optional, 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 | array-like, default False) – 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. For sparse input this option is always True to preserve sparsity.

  • 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 than tol.

  • warm_start (bool, optional) – When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.

  • 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.

  • n_jobs (int or None, default None) – How many jobs to use whenever parallelism is invoked

coef_

Parameter vector (w in the cost function formula).

Type

array, shape (n_features,)

intercept_

Independent term in decision function.

Type

float

n_iter_

Number of iterations run by the coordinate descent solver to reach the specified tolerance.

Type

int | array-like, shape (n_targets,)

selected_alpha_

Penalty chosen through cross-validation, if alpha=’auto’.

Type

float

coef_stderr_

Estimated standard errors for coefficients (see coef_ attribute).

Type

array, shape (n_features,)

intercept_stderr_

Estimated standard error intercept (see intercept_ attribute).

Type

float

__init__(alpha='auto', n_alphas=100, alpha_cov='auto', n_alphas_cov=10, fit_intercept=True, precompute=False, copy_X=True, max_iter=1000, tol=0.0001, warm_start=False, random_state=None, selection='cyclic', n_jobs=None)[source]

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__([alpha, n_alphas, alpha_cov, …])

Initialize self.

coef__interval([alpha])

Get a confidence interval bounding the fitted coefficients.

fit(X, y[, sample_weight, check_input])

Fit debiased lasso model.

get_params([deep])

Get parameters for this estimator.

intercept__interval([alpha])

Get a confidence interval bounding the fitted intercept.

path(*args, **kwargs)

Compute elastic net path with coordinate descent.

predict(X)

Predict using the linear model.

predict_interval(X[, alpha])

Build prediction confidence intervals using the debiased lasso.

prediction_stderr(X)

Get the standard error of the predictions using the debiased lasso.

score(X, y[, sample_weight])

Return the coefficient of determination \(R^2\) of the prediction.

set_params(**params)

Set the parameters of this estimator.

Attributes

sparse_coef_

Sparse representation of the fitted coef_.

coef__interval(alpha=0.1)[source]

Get a confidence interval bounding the fitted coefficients.

Parameters

alpha (float) – The confidence level. Will calculate the alpha/2-quantile and the (1-alpha/2)-quantile of the parameter distribution as confidence interval

Returns

(coef_lower, coef_upper) – Returns lower and upper interval endpoints for the coefficients.

Return type

tuple of arrays, shape (n_coefs, )

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

Fit debiased lasso model.

Parameters
  • X (ndarray or scipy.sparse matrix, (n_samples, n_features)) – Input data.

  • y (array, shape (n_samples,)) – 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.

  • check_input (boolean, (default=True)) – Allow to bypass several input checking. Don’t use this parameter unless you know what you do.

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

intercept__interval(alpha=0.1)[source]

Get a confidence interval bounding the fitted intercept.

Parameters

alpha (float) – The confidence level. Will calculate the alpha/2-quantile and the (1-alpha/2)-quantile of the parameter distribution as confidence interval

Returns

(intercept_lower, intercept_upper) – Returns lower and upper interval endpoints for the intercept.

Return type

tuple floats

static path(*args, **kwargs)

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, 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_outputs)) – Target values.

  • l1_ratio (float, default=0.5) – Number between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). l1_ratio=1 corresponds to the Lasso.

  • 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_outputs), 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).

  • check_input (bool, default=True) – If set to False, the input validation checks are skipped (including the Gram matrix when provided). It is assumed that they are handled by the caller.

  • **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_outputs, 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. (Is returned when return_n_iter is set to True).

See also

MultiTaskElasticNet(), MultiTaskElasticNetCV(), ElasticNet(), ElasticNetCV()

Notes

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

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,)

predict_interval(X, alpha=0.1)[source]

Build prediction confidence intervals using the debiased lasso.

Parameters
  • X (ndarray or scipy.sparse matrix, (n_samples, n_features)) – Samples.

  • alpha (optional float in [0, 1] (Default=0.1)) – The overall level of confidence of the reported interval. The alpha/2, 1-alpha/2 confidence interval is reported.

Returns

(y_lower, y_upper) – Returns lower and upper interval endpoints.

Return type

tuple of arrays, shape (n_samples, )

prediction_stderr(X)[source]

Get the standard error of the predictions using the debiased lasso.

Parameters

X (ndarray or scipy.sparse matrix, (n_samples, n_features)) – Samples.

Returns

prediction_stderr – The standard error of each coordinate of the output at each point we predict

Return type

array like, shape (n_samples, )

score(X, y, sample_weight=None)

Return the coefficient of determination \(R^2\) of the prediction.

The coefficient \(R^2\) 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

property sparse_coef_

Sparse representation of the fitted coef_.