  We study a formalization of the grammar induction problem that models
sentences as being generated by a compound probabilistic context-free grammar.
In contrast to traditional formulations which learn a single stochastic
grammar, our grammar's rule probabilities are modulated by a per-sentence
continuous latent variable, which induces marginal dependencies beyond the
traditional context-free assumptions. Inference in this grammar is performed by
collapsed variational inference, in which an amortized variational posterior is
placed on the continuous variable, and the latent trees are marginalized out
with dynamic programming. Experiments on English and Chinese show the
effectiveness of our approach compared to recent state-of-the-art methods when
evaluated on unsupervised parsing.
