LOCO

class hidimstat.LOCO(estimator, method: str = 'predict', loss: callable = <function mean_squared_error>, statistical_test='ttest', features_groups=None, n_jobs: int = 1)

Bases: BasePerturbation

Leave-One-Covariate-Out (LOCO) algorithm

This method is presented in Lei et al.[1] and Verdinelli and Wasserman[2]. The model is re-fitted for each feature/group of features. The importance is then computed as the difference between the loss of the full model and the loss of the model without the feature/group.

Parameters:

estimatorsklearn compatible estimator

The estimator to use for the prediction.

methodstr, default=”predict”

The method to use for the prediction. This determines the predictions passed to the loss function. Supported methods are “predict”, “predict_proba” or “decision_function”.

losscallable, default=mean_squared_error

The loss function to use when comparing the perturbed model to the full model.

statistical_testcallable or str, default=”ttest”

Statistical test function for computing p-values of importance scores.

features_groups: dict or None, default=None

A dictionary where the keys are the group names and the values are the list of column names corresponding to each features group. If None, the features_groups are identified based on the columns of X.

n_jobsint, default=1

The number of jobs to run in parallel. Parallelization is done over the variables or groups of variables.

Notes

Williamson et al.[3] also presented a LOCO method with an additional data splitting strategy.

References

[1]

Jing Lei, Max G’Sell, Alessandro Rinaldo, Ryan J Tibshirani, and Larry Wasserman. Distribution-free predictive inference for regression. Journal of the American Statistical Association, 113(523):1094–1111, 2018.

[2]

Isabella Verdinelli and Larry Wasserman. Feature importance: a closer look at shapley values and loco. Statistical Science, 39(4):623–636, 2024.

[3]

Brian D. Williamson, Peter B. Gilbert, Noah R. Simon, and Marco Carone. A General Framework for Inference on Algorithm-Agnostic Variable Importance. Journal of the American Statistical Association, 118(543):1645–1658, 2023. doi:10.1080/01621459.2021.2003200.

__init__(estimator, method: str = 'predict', loss: callable = <function mean_squared_error>, statistical_test='ttest', features_groups=None, n_jobs: int = 1)

fit(X, y)

Fit a model after removing each covariate/group of covariates.

Parameters:

Xarray-like of shape (n_samples, n_features)

The training input samples.

yarray-like of shape (n_samples,)

The target values.

Returns:

selfobject

Returns the instance itself.

importance(X, y)

Compute the importance scores for each group of covariates.

Parameters:

Xarray-like of shape (n_samples, n_features)

The input samples to compute importance scores for.

yarray-like of shape (n_samples,)

importances_ndarray of shape (n_groups,)

The importance scores for each group of covariates. A higher score indicates greater importance of that group.

Attributes:

loss_reference_float

The loss of the model with the original (non-perturbed) data.

loss_dict

Dictionary with indices as keys and arrays of perturbed losses as values. Contains the loss values for each permutation of each group.

importances_ndarray of shape (n_groups,)

The calculated importance scores for each group.

pvalues_ndarray of shape (n_groups,)

P-values from one-sided t-test testing if importance scores are significantly greater than 0.

Returns:

importances_ndarray of shape (n_features,)

Importance scores for each feature.

Notes

The importance score for each group is calculated as the mean increase in loss when that group is perturbed, compared to the reference loss. A higher importance score indicates that perturbing that group leads to worse model performance, suggesting those features are more important.

fdr_selection(fdr, fdr_control='bhq', reshaping_function=None, two_tailed_test=False)

Performs feature selection based on False Discovery Rate (FDR) control.

Parameters:

fdrfloat

The target false discovery rate level (between 0 and 1)

fdr_control: {‘bhq’, ‘bhy’}, default=’bhq’

The FDR control method to use: - ‘bhq’: Benjamini-Hochberg procedure - ‘bhy’: Benjamini-Hochberg-Yekutieli procedure

reshaping_function: callable or None, default=None

Optional reshaping function for FDR control methods. If None, defaults to sum of reciprocals for ‘bhy’.

two_tailed_test: bool, default=False

If True, performs two-tailed test selection using both p-values for positive effects and one-minus p-values for negative effects. The sign of the effect is determined from the sign of the importance scores.

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.

Raises:

ValueError

If importances_ haven’t been computed yet

AssertionError

If pvalues_ are missing or fdr_control is invalid

fit_importance(X, y)

Fits the model to the data and computes feature importance scores. Convenience method that combines fit() and importance() into a single call.

Parameters:

Xarray-like of shape (n_samples, n_features)

Training data.

yarray-like of shape (n_samples,)

Target values.

Returns:

importances_ndarray of shape (n_groups,)

The calculated importance scores for each feature group. Higher values indicate greater importance.

Notes

This method first calls fit() to identify feature groups, then calls importance() to compute the importance scores for each group.

fwer_selection(fwer, procedure='bonferroni', n_tests=None, two_tailed_test=False)

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()

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)

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)

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)

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)

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)

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:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

Examples using hidimstat.LOCO

Leave-One-Covariate-Out (LOCO) feature importance with different regression models

Leave-One-Covariate-Out (LOCO) feature importance with different regression models

Variable Selection Under Model Misspecification

Variable Selection Under Model Misspecification