Figure 1

Error in the ρ − δ plane for a measurement matrix of random genomic SNPs ( $\mathit{\rho }=\frac{\mathit{s}}{\mathit{n}}$ and $\mathit{\delta }=\frac{\mathit{n}}{\mathit{p}}$ ). (A) Color corresponds to the normalized error (NE) of the coefficients $\frac{{∥\mathit{x}-\widehat{\mathit{x}}∥}_{\mathit{L}2}}{{∥\mathit{x}∥}_{\mathit{L}2}}$. The black curve is the expected phase boundary between poor and good recovery from [26]. The number of SNPs, p, was fixed at 8,027. The heritability was set to one (noiseless case). The circles correspond to the points (ρ = 0.08, δ = 0.19) (white) and (ρ = 0.125, δ = 0.125) (red) discussed in Measures of selection. (B) Same as panel (A), except that the heritability was set to 0.5 (noisy case). The white circle corresponds to the point (ρ = 0.025, δ = 0.625) discussed in Measures of selection. (C) NE versus ρ for fixed n = 4,000 and p = 8,027 (blue corresponds to h ² = 1, red to h ² = 0.5). The square markers indicate recovery quality evaluated at a few data points using the lasso algorithm with 10-fold cross-validation written by MATLAB.