On Thursday I'll be at the Allen Institute for Brain Science to give a talk (video and slides):
Title: Genetic Architecture and Predictive Modeling of Quantitative Traits
Abstract: I discuss the application of Compressed Sensing (L1-penalized optimization or LASSO) to genomic prediction. I show that matrices comprised of human genomes are good compressed sensors, and that LASSO applied to genomic prediction exhibits a phase transition as the sample size is varied. When the sample size crosses the phase boundary complete identification of the subspace of causal variants is possible. For typical traits of interest (e.g., with heritability ~ 0.5), the phase boundary occurs at N ~ 30s, where s (sparsity) is the number of causal variants. I give some estimates of sparsity associated with complex traits such as height and cognitive ability, which suggest s ~ 10k. In practical terms, these results imply that powerful genomic prediction will be possible for many complex traits once ~ 1 million genotypes are available for analysis.