In Pairwise LiNGAM inference, the candidate linear causal models are evaluated by comparing their fit scores at a fixed complexity. The fit score used for comparison is the likelihood score, derived by Hyvärinen and Smith as:

$S_{X \rightarrow Y} = -\left[\sum_{i=1}^n G_X(x^i)+G_{N_Y}\left(\frac{y^i - \rho x^i}{\sqrt{1-\rho^2}}\right)\right]+n\log (1-\rho^2)$

where $G_X(u) = \log P_X(u)$, and $G_{N_Y}$ is the standardized log probability distribution function of the residual when regressing $Y$ on $X$. The score S_{Y rightarrow X} is computed similarly, and the causal direction is decided by comparing S_{X rightarrow Y} with S_{Y rightarrow X}.