A lasso for hierarchical testing of interactions

We consider the testing of all pairwise interactions in a two-class problem with many features. We devise a hierarchical testing framework that only considers an interaction when one or more of its constituent features has a nonzero main effect. It is based on a convex optimization framework that seamlessly considers main effects and interactions together. We provide examples— both real and simulated– that show a potential gain in power and interpretability over a standard (non-hierarchical) interaction test.

[1]  M. LeBlanc,et al.  Increasing the power of identifying gene × gene interactions in genome‐wide association studies , 2008, Genetic epidemiology.

[2]  Isaac Dialsingh,et al.  Large-scale inference: empirical Bayes methods for estimation, testing, and prediction , 2012 .

[3]  Bradley Efron,et al.  Large-scale inference , 2010 .

[4]  Christian P. Robert,et al.  Large-scale inference , 2010 .

[5]  Mee Young Park,et al.  Penalized logistic regression for detecting gene interactions. , 2008, Biostatistics.

[6]  Low-Tone Ho,et al.  Tree-structured supervised learning and the genetics of hypertension. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[7]  R. Tibshirani,et al.  Significance analysis of microarrays applied to the ionizing radiation response , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[8]  S. Dudoit,et al.  Multiple Testing Procedures with Applications to Genomics , 2007 .

[9]  Carolyn Hutter,et al.  Powerful Cocktail Methods for Detecting Genome‐Wide Gene‐Environment Interaction , 2012, Genetic epidemiology.

[10]  Robert Tibshirani,et al.  A Permutation Approach to Testing Interactions in Many Dimensions , 2012 .

[11]  R. Tibshirani,et al.  A LASSO FOR HIERARCHICAL INTERACTIONS. , 2012, Annals of statistics.

[12]  Kenneth Rice,et al.  Permutation and Parametric Bootstrap Tests for Gene–Gene and Gene–Environment Interactions , 2011, Annals of human genetics.