The Rebane-Pearl polytree algorithm constructs a polytree-shaped belief network approximation to a probability distribution (Rebane and Pearl, 1987).
The Rebane-Pearl algorithm is similar to the Chow-Liu tree algorithm for constructing the “best possible” tree-shaped belief network approximation to a probability distribution such that all edges are directed away from the root. Instead of constructing a tree-shaped belief network approximation, the algorithm constructs a polytree-shaped belief network.
Rebane-Pearl polytree recovery algorithm: The Chow-Liu algorithm constructs a simple tree structure (each node has one parent — except the root). The Rebane-Pearl algorithm turns this tree into a polytree (each node can have multiple parents, but the underlying network structure is still a tree).
Chow, C. N. Liu (1968). Approximating Discrete Probability Distributions with Dependence Trees.
Rebane, J. Pearl, (1987). The recovery of causal polytrees from statistical data.