Independently Interpretable Lasso for Generalized Linear Models

Area of Science:

• Machine Learning
• Statistical Modeling

Background:

• Sparse regularization is effective for high-dimensional problems but sensitive to feature correlations.
• Existing methods like ordinary Lasso can select correlated variables, harming interpretability and estimation.

Purpose of the Study:

• Propose a novel regularization method, Independently Interpretable Lasso (IILasso), for generalized linear models.
• Address the issue of correlated feature selection in sparse regularization.

Main Methods:

• Developed a new regularizer that suppresses the selection of correlated variables.
• Analyzed the theoretical properties of IILasso, focusing on sign recovery and convergence rates.

Main Results:

• IILasso ensures that selected variables affect the response independently, enhancing interpretability.
• Demonstrated theoretical advantages in sign recovery and achieved near-minimax optimal convergence rates.
• Empirical results on synthetic and real data confirm IILasso's effectiveness.

Conclusions:

• IILasso offers improved interpretability and performance over traditional sparse regularization methods.
• The method effectively handles feature correlations, leading to more reliable models.