A country conducts a census survey, including socio-demographic questions (age, gender, education, profession, number of children, salary, etc.). The question is to determine which factor influences which other factor.

The dataset consists of joint answers from $n$ citizens for factor pairs $( X_k , Y_k ), k = 1, ⋯ N : S_k = \{( x_{k 1} , y_{k 1} ), ⋯ , ( x_{kn} , y_{kn} \}$. Prior knowledge allows us to determine the ground truth for a few pairs $( X_k , Y_k )$ (for example age can influence wages and not vice-versa).

This constitutes an empirical “mother distribution” of pairs $\{( S_1 , g_1 ), ⋯ , ( S_k , g_k ), ⋯ , ( S_N , g_N )\}$ from which we might train a classifier to label other similar pairs with their causal direction.