Reflection Knockoffs via Householder Reflection: Applications in Proteomics and Genetic Fine Mapping.

We present a novel knockoff construction method, and demonstrate its superior performance in two applications: identifying proteomic signatures of age and genetic fine mapping. Both applications involve datasets of highly correlated features, but they differ in the abundance of driver associations. Our primary contribution is the invention of the reflection knockoff, which is constructed from mirror images - obtained via Householder reflection - of the original features. The reflection knockoffs substantially outperform Model-X knockoffs in feature selection, particularly when features are highly correlated. Our secondary contribution is a simple method to aggregate multiple sets of identically distributed knockoff statistics to improve the consistency of knockoff filters. In the study of proteomic signatures of age, single feature tests showed overly abundant proteomic association with age. Knockoff filters using reflection knockoffs and aggregation, however, revealed that a majority of these associations are hitchhikers instead of drivers. When applied to genetic fine mapping, knockoff filters using reflection knockoffs and aggregation outperform a state-of-the-art method. We discuss a potentially exciting application of reflection knockoffs: sharing genetic data without raising concerns about privacy and regulatory violations.