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 (str | float, 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, default 100) – How many alphas to try if alpha=’auto’
alpha_cov (str | float, 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, default 10) – How many alpha_cov to try if alpha_cov=’auto’.
fit_intercept (bool, 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 (bool, 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, 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, optional) – 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]

Methods

`__init__`([alpha, n_alphas, alpha_cov, ...])
`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`(X, y, *[, l1_ratio, eps, n_alphas, ...])	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 of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

Attributes

sparse_coef_

Sparse representation of the fitted coef_.

coef__interval(alpha=0.05)[source]

Get a confidence interval bounding the fitted coefficients.

Parameters: alpha (float, default 0.05) – 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 array, 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 (bool, 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=0.05)[source]

Get a confidence interval bounding the fitted intercept.

Parameters: alpha (float, default 0.05) – 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(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)

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.