How Many Samples Are Needed to Determine Causal Direction? Sharp Minimax Bounds for Bivariate LiNGAM

Excerpt

arXiv:2608.15840v1 Announce Type: cross Abstract: We study how many observations are needed to determine the causal direction between two linearly related variables. Classical LiNGAM theory shows that independent non-Gaussian disturbances identify the direction, but does not quantify the difficulty when the causal effect is weak or the disturbances are nearly Gaussian. Let $\beta$ bound the absolute structural coefficient from below, let $\nu$ measure each standardized disturbance's distance fro