= Latent projection
A <latent projection> represents the influence of unobserved vertices of a <directed acyclic graph> on its observed vertices using an <acyclic directed mixed graph>. It retains an arrow $a\to b$ when the original graph has a directed path from $a$ to $b$ whose internal vertices are all unobserved. It adds $a\leftrightarrow b$ when there is a path with arrowheads at both observed endpoints whose internal vertices are unobserved noncolliders.
For example, the hidden fork $A\leftarrow U\to B$ becomes $A\leftrightarrow B$, while $A\to U\to B$ becomes $A\to B$. The bidirected edge encodes latent common-cause structure, not two opposing causal effects. Both edge types may coexist between a pair. The construction preserves the appropriate observed separation relations, while retaining more useful structure than simply deleting hidden vertices and their edges.<Nested Markov Properties for Acyclic Directed Mixed Graphs by Thomas S. Richardson and others>[Section on latent projections of directed acyclic graphs]{ref}
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