  We construct genomic predictors for heritable and extremely complex human
quantitative traits (height, heel bone density, and educational attainment)
using modern methods in high dimensional statistics (i.e., machine learning).
Replication tests show that these predictors capture, respectively, $\sim$40,
20, and 9 percent of total variance for the three traits. For example,
predicted heights correlate $\sim$0.65 with actual height; actual heights of
most individuals in validation samples are within a few cm of the prediction.
The variance captured for height is comparable to the estimated SNP
heritability from GCTA (GREML) analysis, and seems to be close to its
asymptotic value (i.e., as sample size goes to infinity), suggesting that we
have captured most of the heritability for the SNPs used. Thus, our results
resolve the common SNP portion of the "missing heritability" problem -- i.e.,
the gap between prediction R-squared and SNP heritability. The $\sim$20k
activated SNPs in our height predictor reveal the genetic architecture of human
height, at least for common SNPs. Our primary dataset is the UK Biobank cohort,
comprised of almost 500k individual genotypes with multiple phenotypes. We also
use other datasets and SNPs found in earlier GWAS for out-of-sample validation
of our results.
