Fig. 2

a Comparative assessment of model performance on held-out data for MMM and SIGMA across different distance thresholds. SIGMA at a threshold of 2000 bp shows the best performance by maximizing the log-likelihood (the y-axis has a customized scale with a scale break). b Comparison of fraction of signature 1 mutations found in CpG islands in sky and clouds. Both NMF and SIGMA show significant depletion of signature 1 in CpG islands with respect to randomized data, with SIGMA exhibiting more pronounced depletions, particularly in clouds. We performed 1000 permutations of signature assignments preserving mutation trinucleotide context within each sample. We used a one-sided Wilcoxon signed-rank test to compare the observed and randomized numbers of signature 1 in CpG islands. c Spearman correlation comparison of APOBEC3A/B expression with signature 2 and 13 activities across samples. For signature 2, the mutation counts in clouds with SIGMA are positively correlated with APOBEC3A/B expression while the NMF-based counts have zero or negative correlation in both sky and clouds. Signature 13 mutation counts are positively correlated in both models. In b and c, the significance level was categorized as *P value (P) < 0.05; ** P<5×10⁻³; *** P<5×10⁻⁵. All bar plots show mean values with standard error of the mean (small black bars) from 31 random initializations of MMM and SIGMA models