Convex Modeling of Interactions with Strong Heredity

• Activity Number: 504
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Asad Haris* and Daniela Witten and Noah Simon
• Companies: and University of Washington and University of Washington
• Keywords: Interaction models ; Strong heredity ; Penalized regression ; Convex penalty ; Convex optimization ; ADMM

Abstract

We consider the task of fitting a regression model involving interactions among a potentially large set of covariates, in which we wish to enforce strong heredity. We propose FAMILY, a general framework for this task which is a generalization of several existing methods. It can be formulated as the solution to a convex optimization problem, which we solve using an efficient alternating directions method of multipliers (ADMM) algorithm. This algorithm has guaranteed convergence to the global optimum, can be easily specialized to any convex penalty function of interest, and allows for a straightforward extension to the setting of generalized linear models. We derive an unbiased estimator of the degrees of freedom of FAMILY, and explore its performance in a simulation study and on an HIV sequence data set.