Naturally-occurring bracketings, such as answer fragments to natural language questions and hyperlinks on webpages, can reflect human syntactic intuition regarding phrasal boundaries. Their availability and approximate correspondence to syntax make them appealing as distant information sources to incorporate into unsupervised constituency parsing. But they are noisy and incomplete; to address this challenge, we develop a partial-brackets-aware structured ramp loss in learning. Experiments demonstrate that our distantly-supervised models trained on naturally-occurring bracketing data are more accurate in inducing syntactic structures than competing unsupervised systems. On the English WSJ corpus, our models achieve an unlabeled F1 score of 68.9 for constituency parsing.
We present symbolic and numerical methods for computing Poisson brackets on the spaces of measures with positive densities of the plane, the 2-torus, and the 2-sphere. We apply our methods to compute symplectic areas of finite regions for the case of the 2-sphere, including an explicit example for Gaussian measures with positive densities.