Unsupervised constituency parsing has been explored much but is still far from being solved. Conventional unsupervised constituency parser is only able to capture the unlabeled structure of sentences. Towards unsupervised full constituency parsing, we propose an unsupervised and training-free labeling procedure by exploiting the property of a recently introduced metric, Neighboring Distribution Divergence (NDD), which evaluates semantic similarity between sentences before and after editions. For implementation, we develop NDD into Dual POS-NDD (DP-NDD) and build "molds" to detect constituents and their labels in sentences. We show that DP-NDD not only labels constituents precisely but also inducts more accurate unlabeled constituency trees than all previous unsupervised methods with simpler rules. With two frameworks for labeled constituency trees inference, we set both the new state-of-the-art for unlabeled F1 and strong baselines for labeled F1. In contrast with the conventional predicting-and-evaluating scenario, our method acts as an plausible example to inversely apply evaluating metrics for prediction.
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