Extended Data Fig. 2: Within-sample accuracy of LDGM precision matrices.

a-c, Boxplots showing the error of the LDGM precision matrix. d-f, Boxplots showing the error of the identity matrix. Three different error metrics were used. Boxplots indicate the median, quartiles and range for the 20 LD blocks on chromosome 22, for each 1000 Genomes ancestry group. a and d show the mean-squared error (see Methods). b and e show the mean-squared error after restricting to SNP pairs with a correlation of r² > 0.01. c and f show the alternative mean-squared error, defined as m⁻² Tr((I−PR)(I−RP)). This measures the difference between PR, the product of the LD correlation matrix and the LDGM precision matrix, and the identity matrix (see Supplementary Note, section 4). Compared with the MSE, the alternative MSE is less sensitive to large eigenvalues of R, probably explaining why it is not elevated for AMR. For the identity matrix, the alternative MSE and the MSE are identical. In all plots, the lower whisker, lower hinge, center, upper hinge and upper whisker correspond to (lower hinge − 1.5× interquartile range (IQR)) and the 25th percentile, median, 75th percentile, and (upper hinge + 1.5× IQR), respectively.