  Genome-Wide Association Studies (GWAS) explain only a small fraction of
heritability for most complex human phenotypes. Genomic heritability estimates
the variance explained by the SNPs on the whole genome using mixed models and
accounts for the many small contributions of SNPs in the explanation of a
phenotype.
  This paper approaches heritability from a machine learning perspective, and
examines the close link between mixed models and ridge regression. Our
contribution is twofold. First, we propose estimating genomic heritability
using a predictive approach via ridge regression and Generalized Cross
Validation (GCV). We show that this is consistent with classical mixed model
based estimation. Second, we derive simple formulae that express prediction
accuracy as a function of the ratio n/p, where n is the population size and p
the total number of SNPs. These formulae clearly show that a high heritability
does not imply an accurate prediction when p>n.
  Both the estimation of heritability via GCV and the prediction accuracy
formulae are validated using simulated data and real data from UK Biobank.
