Current form of genome-wide association studies (GWAS) is inadequate to accurately explain the genetics of complex traits due to the lack of sufficient statistical power. It explores each variant individually, but current studies show that multiple variants with varying effect sizes actually act in a concerted way to develop a complex disease. To address this issue, we have developed an algorithmic framework that can effectively solve the multi-locus problem in GWAS with a very high level of

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... fidence. Our methodology consists of three novel algorithms based on graph theory and machine learning. It identifies a set of highly discriminating variants that are stable and robust with little (if any) spuriousness. Consequently, likely these variants should be able to interpret missing heritability of a convoluted disease as an entity. Results: To demonstrate the efficacy of our proposed algorithms, we have considered astigmatism case-control GWAS dataset. Astigmatism is a common eye condition that causes blurred vision because of an error in the shape of the cornea. The cause of astigmatism is not entirely known but a sizable inheritability is assumed. Clinical studies show that developmental disorders (such as, autism) and astigmatism co-occur in a statistically significant number of individuals. By performing classical GWAS analysis, we didn't find any genome-wide statistically significant variants. Conversely, we have identified a set of stable, robust, and highly predictive variants that can together explain the genetics of astigmatism. We have performed a set of biological enrichment analyses based on gene ontology (GO) terms, disease ontology (DO) terms, biological pathways, network of pathways, and so forth to manifest the accuracy and novelty of our findings. Conclusions: Rigorous experimental evaluations show that our proposed methodology can solve GWAS multi-locus problem effectively and efficiently. It can identify signals from the GWAS dataset having small number of samples with a high level of accuracy. We believe that the proposed methodology based on graph theory and machine learning is the most comprehensive one compared to any other machine learning based tools in this domain.