A central goal of our Genetic Signatures Project is to identify combinations of gene variants that can be used to improve human disease diagnosis. The project uses as the input High-density genetic definition data, called Single Nucleotide Polymorphisms (SNPs). There are approximately 360,000 SNPs for the kidney disease dataset we are investigating. GPU-enabled software was published to conduct a genome-wide search for interacting SNP pairs. However, third-order and higher-order interactions have been recognized as a challenge in both statistical and computational senses. Our goal of detecting high order combination of genetic variants is an advance for the field. The project will need to leverage the technology of supercomputing as well as biostatistics algorithms. Current Bioinformatics Pawsey Petascale Pioneers project (BPPP006) in round 2015 has provided promising milestones for reaching our goal.