Convex hierarchical testing of interactions

@article{Bien2015ConvexHT,
  title={Convex hierarchical testing of interactions},
  author={Jacob Bien and Noah Simon and Robert Tibshirani},
  journal={The Annals of Applied Statistics},
  year={2015},
  volume={9},
  pages={27-42}
}
We consider the testing of all pairwise interactions in a two-class problem with many features. We devise a hierarchical testing framework that considers an interaction only when one or more of its constituent features has a nonzero main effect. The test is based on a convex optimization framework that seamlessly considers main effects and interactions together. We show—both in simulation and on a genomic dataset from the SAPPHIRe study—a potential gain in power and interpretability over a… 

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References

SHOWING 1-10 OF 12 REFERENCES
A Permutation Approach to Testing Interactions in Many Dimensions
TLDR
A permutation-based method for testing marginal interactions with a binary response that finds apparent signal and tells a believable story, while logistic regression does not and gives asymptotic consistency results under not too restrictive assumptions.
A LASSO FOR HIERARCHICAL INTERACTIONS.
TLDR
A precise characterization of the effect of this hierarchy constraint is given, a bound on this estimate reveals the amount of fitting "saved" by the hierarchy constraint, and it is proved that hierarchy holds with probability one.
Penalized logistic regression for detecting gene interactions.
TLDR
This work proposes using a variant of logistic regression with (L)_(2)-regularization to fit gene-gene and gene-environment interaction models and demonstrates that this method outperforms other methods in the identification of the interaction structures as well as prediction accuracy.
Permutation and Parametric Bootstrap Tests for Gene–Gene and Gene–Environment Interactions
TLDR
It is shown that in genetic association studies it is not typically possible to construct exact permutation tests of gene‐gene or gene‐environment interaction hypotheses, and an alternative to the permutation approach in testing for interaction, a parametric bootstrap approach is described.
Increasing the power of identifying gene × gene interactions in genome‐wide association studies
TLDR
It is found that for most plausible interaction effects a two‐stage analysis can dramatically increase the power to identify interactions compared to a single-stage analysis based on simulation studies using known genetic models and data from existing genome‐wide association studies.
Powerful Cocktail Methods for Detecting Genome‐Wide Gene‐Environment Interaction
TLDR
This article presents a module‐based approach to integrating various methods that exploits each method's most appealing aspects and develops two novel “cocktail” methods for genome‐wide detection of gene‐environment interactions.
Multiple Testing Procedures with Applications to Genomics
TLDR
This chapter discusses single-Step Multiple Testing Procedures for Controlling General Type I Error Rates, as well asmentation and resampling-Based Empirical Bayes multiple testing procedures forcontrolling Generalized Tail Probability Error Rates.
Large-scale inference
TLDR
This book discusses empirical Bayes and the James-Stein estimator, as well as large-scale hypothesis testing algorithms, and prediction and effect size estimation.
Statistical Power of Model Selection Strategies for Genome-Wide Association Studies
TLDR
A novel statistical approach for power calculation is developed, accurate formulas for the power of different model selection strategies are derived, and the formulas are utilized to evaluate and compare these strategies in genetic model spaces.
Tree-structured supervised learning and the genetics of hypertension.
  • Jing HuangA. Lin R. Olshen
  • Computer Science
    Proceedings of the National Academy of Sciences of the United States of America
  • 2004
TLDR
An algorithm for general supervised learning that extends the binary tree-structured approach although it differs greatly in its selection and combination of predictors, FlexTree seems better than the other technologies in terms of Bayes risk.
...
...