Fig. 1

Description of the KIRCLE methodology. a Flowchart describing the 4 steps of the KIRCLE algorithm as it processes a single KIR gene (KIR2DL1 as an example here). Inputs are green, computations are blue, and outputs are gold. KIRCLE hyperparameters are listed in parentheses where they are implemented. b Depiction of step 4 of KIRCLE (thresholding). Allele probabilities generated by expectation-maximization may lead to a homozygous solution, a heterozygous solution, or no solution at all, depending on the user-selected value of the threshold hyperparameter t. In the depicted example, running KIRCLE with t = 0.5 (blue) would generate a homozygous solution (2 copies of KIR2DL2*003), whereas using t = 0.2 (green) would generate a heterozygous solution (1 copy each of KIR2DL2*002 and KIR2DL2*003). Using t = 0.8 (red) or t = 0.05 (purple) would have yielded no solution. c Depiction of one step of expectation-maximization. The initial allele-read matrix \({M}^{t_0}\) is collapsed into an expectation vector \({E}^{t_0}\) that is used to compute the next iteration of the matrix \({M}^{t_1}\). This process is repeated until the convergence criterion is satisfied, at which point the final expectation vector represents an estimate of KIR allele probabilities