A Pliable Lasso.

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• The standard lasso provides a robust method for feature selection and regularization in high-dimensional data.
• However, it assumes fixed coefficients, limiting its ability to capture complex relationships where effects vary across subgroups or over time.

Purpose of the Study:

• To propose a novel generalization of the lasso that allows model coefficients to vary as a function of prespecified modifying variables.
• To develop a computationally efficient algorithm for estimating this varying coefficient model, incorporating exact screening rules for large datasets.

Main Methods:

• A hierarchical estimation approach is employed to manage degrees of freedom and prevent overfitting.
• The proposed method models each lasso coefficient as a sparse linear function of modifying variables (e.g., gender, age, time).
• The modifying variables can be observed, partially observed, or entirely unobserved.

Main Results:

• The generalization effectively captures dynamic coefficient variations, offering improved model flexibility.
• A computationally efficient algorithm with exact screening rules is presented, enabling scalability to large numbers of predictors.
• The method demonstrates strong performance on both simulated and real-world datasets.

Conclusions:

• The proposed varying coefficient lasso offers a powerful and flexible extension to the standard lasso.
• It provides a principled way to incorporate interactions and subgroup effects, enhancing model interpretability and predictive performance.
• The efficient algorithm facilitates its application in diverse scientific and data-intensive fields.