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Doubly sparse regression incorporating graphical structure among predictors
Author(s) -
Stephenson Matthew,
Ali R. Ayesha,
Darlington Gerarda A.
Publication year - 2019
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11521
Subject(s) - robustness (evolution) , computer science , graphical model , regression , regression analysis , linear regression , graph , representation (politics) , data set , data mining , artificial intelligence , machine learning , statistics , mathematics , theoretical computer science , biochemistry , chemistry , politics , political science , law , gene
Recent research has demonstrated that information learned from building a graphical model on the predictor set of a regularized linear regression model can be leveraged to improve prediction of a continuous outcome. In this article, we present a new model that encourages sparsity at both the level of the regression coefficients and the level of individual contributions in a decomposed representation. This model provides parameter estimates with a finite sample error bound and exhibits robustness to errors in the input graph structure. Through a simulation study and the analysis of two real data sets, we demonstrate that our model provides a predictive benefit when compared to previously proposed models. Furthermore, it is a highly flexible model that provides a unified framework for the fitting of many commonly used regularized regression models. The Canadian Journal of Statistics 47: 729–747; 2019 © 2019 Statistical Society of Canada