We describe an approach to speed-up inference with latent-variable PCFGs, which have been shown to be highly effective for natural language parsing. Our approach is based on a tensor formulation recently introduced for spectral estimation of latent-variable PCFGs coupled with a tensor decomposition algorithm well-known in the multilinear algebra literature. We also describe an error bound for this approximation, which gives guarantees showing that if the underlying tensors are well approximated, then the probability distribution over trees will also be well approximated. Empirical evaluation on real-world natural language parsing data demonstrates a significant speed-up at minimal cost for parsing performance.
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