Pharmaceutical companies are interested in determining the influence of genes on each other. A dataset may consist of jointly recorded gene activities for $N$ pairs of genes $( X_k , Y_k ), k = 1, ⋯ N$ and for $n$ patients $S_k = \{( x_{k1} , y_{k 1 }), ⋯ , ( x_{ kn} , y_{kn} \}$.

Determining which gene influences which other gene is a costly experimental process, so only a subset of pairs of genes are generally labeled with ground truth of causal relationship $G = g_k$ .

The labeled dataset $\{( S_1 , g_1 ), ⋯ , ( S_k , g_k ), ⋯\}, k = 1⋯ N$ , is an empirical sample of the “mother distribution” over pairs of genes and their causal labels, which may be used as training data to obtain a classifier, such that predictions of unknown causal labels can be made on new pairs of genes.