To illustrate a mother distribution in causal discovery, consider an ecological study conducted to understand a forest ecosystem and preserve biodiversity. The objective is to determine which factor influences which other factor. The dataset consists of $n$ jointly recorded values of many variables $(X_k, Y_k)$, where $k = 1, \dots, N$, in different locations (measuring factors such as soil, humidity, lighting, or the presence of certain plants or animals). This results in samples $S_k = \{ (x_{k1}, y_{k1}), \dots, (x_{kn}, y_{kn}) \}$. Determining which factor influences another is a complicated process; however, prior knowledge of physics and biology may allow researchers to label some pairs with ground truth $G = g_k$ (for example, the aspect of a slope can influence hill shade, but not vice versa). The labeled dataset thus obtained, $\{ (S_1, g_1), \dots, (S_N, g_N) \}$, is an empirical sample of the "mother distribution". It is hoped that more pairs can be automatically labeled using a classifier trained on such data, provided the mechanisms of the other pairs bear some similarity.