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

High heritability does not imply accurate prediction under the small additive effects hypothesis