Leveraging the Predictor Structure with a Doubly Sparse Penalty Function to Improve Outcome Prediction and Relevant Predictor Identification

• Activity Number: 97 - New Methods for Structured Variable Selection
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: SSC (Statistical Society of Canada)
• Author(s): Matthew Stephenson* and Ayesha Ali and Gerarda Darlington
• Companies: University of New Brunswick - Saint John and University of Guelph and University of Guelph
• Keywords: Regularized regression; Prediction; High­-dimensional data; Graphical models; Variable selection

Abstract

Exploiting the structure of complex systems can be advantageous to both accurate outcome prediction and identification of the relevant predictors. The doubly sparse regression incorporating graphical structure among predictors (DSRIG) model for a continuous outcome and its logistic regression counterpart (DSLRIG) for a binary outcome present two such methods. These methods work by first modelling the predictor structure using an undirected graph and then using the resulting neighbourhood structure to define a set of (overlapping) groups. Sparsity is encouraged both within and among the groups that contribute to the overall estimation of the regression parameters. These models are highly flexible and result in superior predictive ability and accuracy in identification of relevant predictors when compared to other previously proposed methods. They also are valid in both the high-dimensional setting and in the presence of multicollinearity. The doubly sparse framework presents the potential to be extended to additional outcome types including the multi-task setting for correlated outcomes and the time-to-event setting.