Optimizing Spectral Learning for Parsing

We describe a search algorithm for optimizing the number of latent states when estimating latent-variable PCFGs with spectral methods. Our results show that contrary to the common belief that the number of latent states for each nonterminal in an L-PCFG can be decided in isolation with spectral methods, parsing results significantly improve if the number of latent states for each nonterminal is globally optimized, while taking into account interactions between the different nonterminals. In addition, we contribute an empirical analysis of spectral algorithms on eight morphologically rich languages: Basque, French, German, Hebrew, Hungarian, Korean, Polish and Swedish. Our results show that our estimation consistently performs better or close to coarse-to-fine expectation-maximization techniques for these languages.