Recently, these has been a surge on studying how to obtain partially annotated data for model supervision. However, there still lacks a systematic study on how to train statistical models with partial annotation (PA). Taking dependency parsing as our case study, this paper describes and compares two straightforward approaches for three mainstream dependency parsers. The first approach is previously proposed to directly train a log-linear graph-based parser (LLGPar) with PA based on a forest-based objective. This work for the first time proposes the second approach to directly training a linear graph-based parse (LGPar) and a linear transition-based parser (LTPar) with PA based on the idea of constrained decoding. We conduct extensive experiments on Penn Treebank under three different settings for simulating PA, i.e., random dependencies, most uncertain dependencies, and dependencies with divergent outputs from the three parsers. The results show that LLGPar is most effective in learning from PA and LTPar lags behind the graph-based counterparts by large margin. Moreover, LGPar and LTPar can achieve best performance by using LLGPar to complete PA into full annotation (FA).
The inside-outside algorithm for inferring the parameters of a stochastic context-free grammar is extended to take advantage of constituent information in a partially parsed corpus. Experiments on formal and natural language parsed corpora show that the new algorithm can achieve faster convergence and better modelling of hierarchical structure than the original one. In particular, over 90 of the constituents in the most likely analyses of a test set are compatible with test set constituents for a grammar trained on a corpus of 700 hand-parsed part-of-speech strings for ATIS sentences.