A Pliable Lasso. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Tibshirani, Robert; Friedman, Jerome
• Is Part Of: Journal of computational and graphical statistics. Volume 29:Issue 1(2020)
• Page Start: 215
• Page End: 225
• Publication Date: 2020-01-02
• Subjects: Interactions -- Linear regression -- Regularization; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2019.1648271
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: We propose a generalization of the lasso that allows the model coefficients to vary as a function of a general set of some prespecified 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. Supplementary materials for this article are available online.