After a brief review (suitable for physicists) of computational genomics and complex traits, I describe recent progress in this area.
Using methods from Compressed Sensing (L1-penalized regression; Donoho-Tanner phase transition with noise) and the UK BioBank dataset of 500k SNP genotypes, we construct genomic predictors for several complex traits. Our height predictor captures nearly all of the predicted SNP heritability for this trait -- thereby resolving the missing heritability problem. Actual heights of most individuals in validation tests are within a few cm of predicted heights. I also discuss application of these methods to cognitive ability and polygenic disease risk: sparsity estimates (of the number of causal loci), combined with phase transition scaling analysis, allow estimates of the amount of data required to construct good predictors.