DesparsifiedLasso#

class hidimstat.DesparsifiedLasso(estimator=None, centered=True, dof_ajdustement=False, model_x=None, preconfigure_model_x_path=True, alpha_max_fraction=0.01, random_state=None, save_model_x=False, tolerance_reid=0.0001, noise_method='AR', order=1, stationary=True, confidence=0.95, distribution='norm', epsilon_pvalue=1e-14, test='chi2', covariance=None, n_jobs=1, memory=None, verbose=0)[source]#

Bases: BaseVariableImportance

Desparsified Lasso Estimator (also known as Debiased Lasso)

Statistical inference in high-dimensional regression using the desparsified Lasso. Provides debiased coefficient estimates, confidence intervals and p-values. Algorithm based on Algorithm 1 of d-Lasso and d-MTLasso in Chevalier[1].

Parameters:

estimatorLassoCV or MultiTaskLassoCV instance, default=None: Initial model for selecting relevant features. Must implement fit and predict. For single task use LassoCV, for multi-task use MultiTaskLassoCV. Set to LassoCV() if None is passed.
model_xLasso or MultiTaskLasso instance, default=None: Base model for nodewise regressions. Set to Lasso() if None is passed.
centeredbool, default=True: Whether to center X and y before fitting.
dof_ajdustementbool, default=False: Whether to apply degrees of freedom adjustment for small samples.
preconfigure_model_x_path: bool, default=True: Whether to preconfigure model_x with n_jobs and random_state.
alpha_max_fractionfloat, default=0.01: Only used if preconfigure_model_x_path is True. Fraction of maximum alpha to use when alphas=None.
random_stateint or RandomState, default=None: Controls randomization.
save_model_xbool, default=False: Whether to save fitted nodewise regression models.
tolerance_reidfloat, default=1e-4: Convergence tolerance for noise estimation.
noise_method{‘AR’, ‘median’}, default=’AR’: Method for noise covariance estimation: - ‘AR’: Autoregressive model - ‘median’: Median correlation
orderint, default=1: Order of AR model if noise_method=’AR’.
stationarybool, default=True: Whether to assume stationary noise.
confidencefloat, default=0.95: Confidence level for intervals.
distributionstr, default=’norm’: Distribution for p-values, only ‘norm’ supported.
epsilon_pvaluefloat, default=1e-14: Small constant to avoid numerical issues.
test{‘chi2’, ‘F’}, default=’chi2’: Test statistic for p-values: - ‘chi2’: Chi-squared test (large samples) - ‘F’: F-test (small samples)
covariancendarray or None, default=None: Pre-specified noise covariance matrix.
n_jobsint, default=1: Number of parallel jobs.
memorystr or Memory, default=None: Cache for intermediate results.
verboseint, default=0: Verbosity level.

Attributes:

importances_ndarray of shape (n_features): Debiased coefficient estimates.
pvalues_ndarray of shape (n_features): Two-sided p-values.
pvalues_corr_ndarray of shape (n_features): Multiple testing corrected p-values.
sigma_hat_float or ndarray of shape (n_task, n_task): Estimated noise level.
precision_diagonal_ndarray of shape (n_features): Diagonal entries of precision matrix.
confidence_bound_min_ndarray of shape (n_features): Lower confidence bounds.
confidence_bound_max_ndarray of shape (n_features): Upper confidence bounds.

__init__(estimator=None, centered=True, dof_ajdustement=False, model_x=None, preconfigure_model_x_path=True, alpha_max_fraction=0.01, random_state=None, save_model_x=False, tolerance_reid=0.0001, noise_method='AR', order=1, stationary=True, confidence=0.95, distribution='norm', epsilon_pvalue=1e-14, test='chi2', covariance=None, n_jobs=1, memory=None, verbose=0)[source]#

fit(X, y)[source]#

Fit the Desparsified Lasso model.

This method fits the Desparsified Lasso model to provide debiased coefficient estimates and statistical inference for high-dimensional regression.

Parameters:

Xarray-like of shape (n_samples, n_features): Training data matrix.
yarray-like of shape (n_samples,) or (n_samples, n_task): Target values. For single task, y should be 1D. For multi-task, y should be 2D with shape (n_samples, n_task).

Returns:

selfobject: Returns the instance with fitted attributes: - importances_ : Desparsified coefficient estimates - sigma_hat_ : Estimated noise level - precision_diagonal_ : Diagonal of precision matrix - clf_ : Fitted nodewise regression models (if save_model_x=True)

Notes

The fitting process: 1. Centers X and y if self.centered=True 2. Fits initial Lasso using cross-validation 3. Estimates noise variance using Reid method 4. Computes nodewise Lasso regressions in parallel 5. Calculates debiased coefficients and precision matrix

importance(X=None, y=None)[source]#

Compute desparsified lasso estimates, confidence intervals and p-values.

Uses fitted model to calculate debiased coefficients along with confidence intervals and p-values. For single task regression, provides confidence intervals based on Gaussian approximation. For multi-task case, computes chi-squared or F test p-values.

Parameters:

Xarray-like of shape (n_samples, n_features): Input data matrix.
yarray-like of shape (n_samples,) or (n_samples, n_task): Target values. For single task, y should be 1D or (n_samples, 1). For multi-task, y should be 2D with shape (n_samples, n_task).

Returns:

importances_ndarray of shape (n_features,) or (n_features, n_task): Desparsified lasso coefficient estimates.

Notes

Updates several instance attributes: - importances_: Desparsified coefficient estimates - pvalues_: Two-sided p-values - pvalues_corr_: Multiple testing corrected p-values - confidence_bound_min_: Lower confidence bounds (single task only) - confidence_bound_max_: Upper confidence bounds (single task only)

For multi-task case, p-values are based on chi-squared or F tests, configured by the test parameter (‘chi2’ or ‘F’).

fit_importance(X, y)[source]#

Fit and compute variable importance in one step.

Parameters:

Xarray-like of shape (n_samples, n_features): Training data matrix.
yarray-like of shape (n_samples,) or (n_samples, n_task): Target values. For single task, y should be 1D or (n_samples, 1). For multi-task, y should be (n_samples, n_task).

Returns:

importances_ndarray of shape (n_features,) or (n_features, n_task): Desparsified lasso coefficient estimates.

fdr_selection(fdr, fdr_control='bhq', reshaping_function=None, two_tailed_test=True)[source]#: Overrides the signature to set two_tailed_test=True by default.

fwer_selection(fwer, procedure='bonferroni', n_tests=None, two_tailed_test=False)[source]#

Performs feature selection based on Family-Wise Error Rate (FWER) control.

Parameters:

fwerfloat: The target family-wise error rate level (between 0 and 1)
procedure{‘bonferroni’}, default=’bonferroni’: The FWER control method to use: - ‘bonferroni’: Bonferroni correction
n_testsint or None, default=None: Factor for multiple testing correction. If None, uses the number of clusters or the number of features in this order.
two_tailed_testbool, default=False: If True, uses the sign of the importance scores to indicate whether the selected features have positive or negative effects.

Returns:

selectedndarray of int: Integer array indicating the selected features. 1 indicates selected features with positive effects, -1 indicates selected features with negative effects, 0 indicates non-selected features.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest: A MetadataRequest encapsulating routing information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

importance_selection(k_best=None, percentile=None, threshold_max=None, threshold_min=None)[source]#

Selects features based on variable importance.

Parameters:

k_bestint, default=None: Selects the top k features based on importance scores.
percentilefloat, default=None: Selects features based on a specified percentile of importance scores.
threshold_maxfloat, default=None: Selects features with importance scores below the specified maximum threshold.
threshold_minfloat, default=None: Selects features with importance scores above the specified minimum threshold.

Returns:

selectionarray-like of shape (n_features,): Binary array indicating the selected features.

plot_importance(ax=None, ascending=False, feature_names=None, **seaborn_barplot_kwargs)[source]#

Plot feature importances as a horizontal bar plot.

Parameters:

axmatplotlib.axes.Axes or None, (default=None): Axes object to draw the plot onto, otherwise uses the current Axes.
ascending: bool, default=False: Whether to sort features by ascending importance.
**seaborn_barplot_kwargsadditional keyword arguments: Additional arguments passed to seaborn.barplot. https://seaborn.pydata.org/generated/seaborn.barplot.html

Returns:

axmatplotlib.axes.Axes: The Axes object with the plot.

pvalue_selection(k_lowest=None, percentile=None, threshold_max=0.05, threshold_min=None, alternative_hypothesis=False)[source]#

Selects features based on p-values.

Parameters:

k_lowestint, default=None: Selects the k features with lowest p-values.
percentilefloat, default=None: Selects features based on a specified percentile of p-values.
threshold_maxfloat, default=0.05: Selects features with p-values below the specified maximum threshold (0 to 1).
threshold_minfloat, default=None: Selects features with p-values above the specified minimum threshold (0 to 1).
alternative_hypothesisbool, default=False: If True, selects based on 1-pvalues instead of p-values.

Returns:

selectionarray-like of shape (n_features,): Binary array indicating the selected features (True for selected).

set_params(**params)[source]#

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: