The mother distribution is a distribution over joint distributions of pairs of variables. The authors adopt the following definition of a mother distribution: A mother distribution $P_M( P_{Π = π} ( X , Y ), G = g )$ is a distribution over pairs $( P_{Π = π} ( X , Y ), G = g )$, where $Π$ and $G$ are random variables: - $Π = π$ indexes distribution $P_{Π = π} ( X , Y )$ over random variables $X$ and $Y$; $π$ may possibly take an infinite number of values (e.g. parameters of a generative process) - $G = g$ labels causal relationship, $g ∈ \{ X → Y , X ← Y , X \leftrightarrow Y , X ⊥ Y \}$.