Gateaux Differential-Based Boosting for High-Dimensional Grouped Variables with Application of Gene-Gene Interaction

• Activity Number: 289
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Kevin He*+ and Yi Li and Ji Zhu
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Boosting ; Interaction ; Variable selection ; Grouped variables

Abstract

Identifying gene-gene interactions is fundamentally important to clarify genetic pathways that regulate patients' response to treatment. An asymmetric hierarchy is often desirable such that the inclusion of a two-way interaction implies the inclusion of at least one main effect. Owing to the very large number of parameters and the dynamic nature of the candidate set, directly solving this problem with regularization methods is infeasible. To address this problem, we proposed a grouped Gateaux differential-based boosting which can be applied to adapt group structure and identify gene-gene interactions in high dimensional settings. The proposed method has the advantage that the candidate set for variable selection is dynamic, which enforces hierarchy. To add more flexibility, one could also consider all possible second-order interactions as candidate factors. The proposed algorithm can be shown to take the group LARS as special cases. It is more flexible in that it can be applied to loss functions that are more complex than linear least squares and avoids some limitations inherited with the existing constrained optimization methods.