A Pliable Lasso

TL;DR

The paper introduces a flexible extension of the lasso that allows coefficients to vary with auxiliary variables, enabling modeling of complex relationships such as interactions and varying effects.

Contribution

It presents a hierarchical estimation approach for a generalized pliable lasso, incorporating efficient algorithms and screening rules for high-dimensional data.

Findings

Effective in modeling varying effects and interactions

Demonstrated on simulated and real datasets

Controls overfitting through hierarchical estimation

Abstract

We propose a generalization of the lasso that allows the model coefficients to vary as a function of a general set of modifying variables. These modifiers might be variables such as gender, age or time. The paradigm is quite general, with each lasso coefficient modified by a sparse linear function of the modifying variables $Z$. The model is estimated in a hierarchical fashion to control the degrees of freedom and avoid overfitting. The modifying variables may be observed, observed only in the training set, or unobserved overall. There are connections of our proposal to varying coefficient models and high-dimensional interaction models. We present a computationally efficient algorithm for its optimization, with exact screening rules to facilitate application to large numbers of predictors. The method is illustrated on a number of different simulated and real examples.