  We introduce a method for unsupervised parsing that relies on bootstrapping
classifiers to identify if a node dominates a specific span in a sentence.
There are two types of classifiers, an inside classifier that acts on a span,
and an outside classifier that acts on everything outside of a given span.
Through self-training and co-training with the two classifiers, we show that
the interplay between them helps improve the accuracy of both, and as a result,
effectively parse. A seed bootstrapping technique prepares the data to train
these classifiers. Our analyses further validate that such an approach in
conjunction with weak supervision using prior branching knowledge of a known
language (left/right-branching) and minimal heuristics injects strong inductive
bias into the parser, achieving 63.1 F$_1$ on the English (PTB) test set. In
addition, we show the effectiveness of our architecture by evaluating on
treebanks for Chinese (CTB) and Japanese (KTB) and achieve new state-of-the-art
results. Our code and pre-trained models are available at
https://github.com/Nickil21/weakly-supervised-parsing.
