The LDAK weightings are designed to equalize the tagging of SNPs across the genome; SNPs in regions of high linkage disquilbirum (LD) will tend to get low weightings, and vice versa. The way LDAK calculates the weightings is described in full in our paper **Improved heritability estimation from genome-wide SNPs** (AJHG, 2012). However, very briefly, the method first assesses patterns of local LD by calculating a matrix of local pairwise squared-correlations between SNPs. Row i of this matrix will indicate to what extent the signal of SNP i is replicated by its neighbouring SNPs, so that the sum of these values will reflect the total amount that the signal of SNP i is replicated. Based on this matrix, LDAK determines SNP weightings so that the sum of the values in Row i times the SNP weightings equals (approximately) one. Originally, these weightings were calculated using the simplex method (linear optimization), however, we subsequently switched to a quadratic solver (the two approaches results in very similar weightings, but the latter is more efficient).

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The following picture describes the intuition behind the LDAK weightings.

In this toy example, there are nine SNPs, X_{1}, X_{2}, ..., X_{9}, with corresponding weightings w_{1}, w_{2},..., w_{9}. SNPs 1 & 2 are highly correlated, as are SNPs 4 & 5, and also SNPs 6, 7, 8 & 9. Therefore, we view the nine SNPs as tagging only four distinct sources of underlying variation (U_{1}, U_{2}, U_{3} & U_{4}). If the SNPs were weighted evenly, then U_{4} would get twice as much weighting as U_{1} & U_{3}, and four times as much weighting as U_{2} (because U_{4} is tagged by twice as many SNPs as U_{1} & U_{3}, and four times as many SNPs as U_{2}). The LDAK weightings might instead set w_{1}=w_{2}=1/2, w_{3}=1, w_{4}=w_{5}=1/2 and w_{6}=w_{7}=w_{8}=w_{9}=1/4, so that the total weighting for each source of underlying variation is one.