  Motivation: Genome-wide association studies (GWASs), which assay more than a
million single nucleotide polymorphisms (SNPs) in thousands of individuals,
have been widely used to identify genetic risk variants for complex diseases.
However, most of the variants that have been identified contribute relatively
small increments of risk and only explain a small portion of the genetic
variation in complex diseases. This is the so-called missing heritability
problem. Evidence has indicated that many complex diseases are genetically
related, meaning these diseases share common genetic risk variants. Therefore,
exploring the genetic correlations across multiple related studies could be a
promising strategy for removing spurious associations and identifying
underlying genetic risk variants, and thereby uncovering the mystery of missing
heritability in complex diseases. Results: We present a general and robust
method to identify genetic patterns from multiple large-scale genomic datasets.
We treat the summary statistics as a matrix and demonstrate that genetic
patterns will form a low-rank matrix plus a sparse component. Hence, we
formulate the problem as a matrix recovering problem, where we aim to discover
risk variants shared by multiple diseases/traits and those for each individual
disease/trait. We propose a convex formulation for matrix recovery and an
efficient algorithm to solve the problem. We demonstrate the advantages of our
method using both synthesized datasets and real datasets. The experimental
results show that our method can successfully reconstruct both the shared and
the individual genetic patterns from summary statistics and achieve better
performance compared with alternative methods under a wide range of scenarios.
