Just as Collins uses rules to identify heads and arguments and thereby lexicalize trees, Chiang uses nearly the same rules to reconstruct derivations: each training example is broken into elementary trees, with each head child remaining attached to its parent, each argument broken into a substitution node and an initial root, and each adjunct broken off as a modifier auxiliary tree.
in this experiment we view the derived trees in the Treebank as incomplete data, and try to reconstruct the derivations (the complete data) using the Inside-Outside algorithm.