PMC

The Model for the Sach's Data estimated by the FASK algorithm.

The “extended expert" model for Sachs's data set). See Sachs et al. () or Ramsey and Bryan () for the significance of the variables.

Illustration of how the PC algorithm works. (A) Original true causal graph. (B) PC starts with a fully-connected undirected graph. (C) The X − Y edge is removed because X ⫫ Y. (D) The X − W and Y − W edges are removed because X ⫫ W |Z and Y ⫫ W |Z. (E) After finding v-structures. (F) After orientation propagation.

IIllustration of how the FCI algorithm is able to determine the existence of latent confunders. (A) Original true causal graph. (B) After edges are removed because of conditional independence relations. (C) The output of FCI, indicating that there is at least one unmeasured confounder of Y and Z.

Illustration of causal asymmetry between two variables with linear relations. The causal relation is X → Y. From top to bottom: X and E both follow the Gaussian distribution (case 1), uniform distribution (case 2), and Laplace distribution (case 3). The two columns on the left show the scatter plot of X and Y and that of X and the regression residual for regressing Y on X, and the two columns on the right correspond to regressing X on Y.