“…Pairwise-based DirectLiNGAM, which uses a simple linear approximation to reduce the computational cost of the likelihood ratio, was later developed [3] . DirectLiNGAM has been applied to various data, such as medical and health data [ 7 , 8 ], metagenome and metabolome data [ 9 , 10 ], and financial data [11] . The background information is detailed in the ‘Additional Information’ section.…”