Biochemistry of the living cell involves multitude of very complex nonlinear interactions between proteins coded for by DNA. Thus the in-silico searches for disease related bio-markers have to consider non-linear interactions between millions of directly measured features such as SNP calls. This poses unprecedented statistical and computational challenges for feature selection and reduction techniques. This paper argues that constructive answers to these challenges are feasible. We focus on presentation of a statistical test for feature selection with sufficient statistical power to overcome principled multiple test correction in an exhaustive evaluation of hundreds of billions of pairwise interactions. For an empirical validation of the methodology we show replication of filtered interactions in multiple independent Genome Wide Association Studies (GWAS) of the same diseases, namely, Celiac and Type 2 Diabetes.