l0l2learn 0.1.0

Cardinality- and budget-constrained feature selection for logistic regression using mixed-integer conic optimization

l0l2learn

Feature selection for logistic regression using mixed-integer conic optimization. Unlike Lasso-based approaches, l0l2learn directly optimizes feature subsets under explicit cardinality or budget constraints.

Overview

l0l2learn is a Python package that provides sklearn-style estimators for cardinality- and budget-constrained feature selection in logistic regression. The package currently includes:

• L0L2Classifier: L0-constrained L2-regularized logistic regression
• ResampledL0L2Classifier: resampling-based feature selection with frequency-based aggregation to improve the selection stability

Installation

To install the package, use the following command:

pip install l0l2learn

Please check the MOSEK website to request and set up a license for the conic solver.

Quick Start

Feature Selection Without Resampling

from sklearn.datasets import load_breast_cancer
from sklearn.metrics import roc_auc_score
from sklearn.model_selection import train_test_split

from l0l2learn import L0L2Classifier


X, y = load_breast_cancer(return_X_y=True, as_frame=True)
X_train, X_test, y_train, y_test = train_test_split(
    X, y, stratify=y
)

clf = L0L2Classifier(
    b=3,
    lambd=1.0
)

clf.fit(X_train, y_train)
y_proba = clf.predict_proba(X_test)

print("ROC AUC:      ", roc_auc_score(y_test, y_proba[:, 1]))
print("Coefficients: ", clf.coef_)
print("Intercept:    ", clf.intercept_)
print("Support:      ", clf.support_)

Feature Selection With Resampling

from sklearn.datasets import load_breast_cancer
from sklearn.metrics import roc_auc_score
from sklearn.model_selection import train_test_split

from l0l2learn import ResampledL0L2Classifier


X, y = load_breast_cancer(return_X_y=True, as_frame=True)
X_train, X_test, y_train, y_test = train_test_split(
    X, y, stratify=y
)

clf = ResampledL0L2Classifier(
    b=3,
    param_grid={"lambd": [1.0]},
    n_resamples=3
)

clf.fit(X_train, y_train)
y_proba = clf.predict_proba(X_test)

print("ROC AUC:      ", roc_auc_score(y_test, y_proba[:, 1]))
print("Coefficients: ", clf.coef_)
print("Intercept:    ", clf.intercept_)
print("Support:      ", clf.support_)
print("VIFs:         ", clf.variable_inclusion_frequencies_[clf.support_])
print("MSFs:         ", clf.model_selection_frequencies_)

Hyperparameters

Feature Costs

Feature-specific costs can be supplied through c:

clf = L0L2Classifier(c=[1, 2, 5])

The optimization then accounts for some variables to be more expensive than others.

Feature Selection Budget

The feature selection budget is controlled through b:

clf = L0L2Classifier(b=5)

When all feature costs are equal to one (the default), b directly controls the maximum number of selected features.

L2 Regularization

The L2 regularization strength is given by lambd:

clf = L0L2Classifier(lambd=0.1)

Larger values can attenuate overfitting and increase robustness.

Number of Resamples

n_resamples determines how many resampled models are fitted:

clf = ResampledL0L2Classifier(b=5, n_resamples=99)

Larger values can improve frequency estimates but increase runtime.

Other Hyperparameters

L0L2Classifier

• fit_intercept: Whether an intercept term is included in the logistic regression model.

• time_limit: Maximum runtime in seconds for the optimization problem.

• mosek_log: Enables printing of MOSEK solver output.

ResampledL0L2Classifier

• resampling: Controls whether and how rows, columns, both, or neither are resampled.

• n_row_subsamples: Number or fraction of observations used during row subsampling.

• n_column_subsamples: Number or fraction of features used during column subsampling.

• aggregation: Whether model selection or variable inclusion frequencies are used for aggregation.

• vif_threshold: Minimum variable inclusion frequency required when using aggregation="VIF".

• estimator: Alternative base estimator used instead of the default L0L2Classifier.

• param_grid: Hyperparameter grid used for cross-validation when tuning lambd.

• cv: Cross-validation strategy used for hyperparameter tuning.

• scoring: Scoring metric used to select the best hyperparameter configuration.

• numerical_features: Specifies which DataFrame columns should be treated as numerical features.

• categorical_features: Specifies which DataFrame columns should be treated as categorical features.

• fit_intercept: Whether an intercept term is included in the logistic regression model.

• mosek_time_limit: Maximum runtime in seconds for each individual optimization problem.

• total_time_limit: Maximum runtime in seconds for the complete resampling procedure.

• max_consecutive_failures: Stops resampling if too many consecutive model fits fail.

• mosek_log: Enables printing of MOSEK solver output.

• n_jobs: Number of parallel workers used during resampling.

• random_state: Controls the randomness of resampling and cross-validation procedures.

License

This project is licensed under the MIT License. See the LICENSE file for details.

Authors

• Ricardo Knauer (HTW Berlin)