I-map

An I-map (independency map) is a concept in Probabilistic graphical models. Although it is not a complicated concept, one needs to carefully analyze the semantics of an I-map otherwise it gets confusing.

An I-map is a function that takes as input a graph $$G$$ and outputs a set whose elements are (conditional) independences in a probability distribution $$P$$ :

$$I(G) = \{(X\perp Y| Z): \text{d-sep}_G(X,Y|Z)\}$$