  We propose a method for unsupervised parsing based on the linguistic notion
of a constituency test. One type of constituency test involves modifying the
sentence via some transformation (e.g. replacing the span with a pronoun) and
then judging the result (e.g. checking if it is grammatical). Motivated by this
idea, we design an unsupervised parser by specifying a set of transformations
and using an unsupervised neural acceptability model to make grammaticality
decisions. To produce a tree given a sentence, we score each span by
aggregating its constituency test judgments, and we choose the binary tree with
the highest total score. While this approach already achieves performance in
the range of current methods, we further improve accuracy by fine-tuning the
grammaticality model through a refinement procedure, where we alternate between
improving the estimated trees and improving the grammaticality model. The
refined model achieves 62.8 F1 on the Penn Treebank test set, an absolute
improvement of 7.6 points over the previous best published result.
