PhD Depth Examination Report Algebraic Foundation of Statistical Parsing Semiring Parsing

Statistical parsing algorithms are useful in structure predictions, ranging from NLP to biological sequence analysis. Currently, there are a variety of efficient parsing algorithms available for different grammar formalisms. Conventionally, different parsing descriptions are needed for different tasks; a fair amount of work is required to construct for each one. Semiring parsing is proposed to provide a generalized and modularized framework to unify all these different parsing algorithms into a general framework and by separation of the algebra and the algorithms, it makes the very same algorithm can perform across diverse tasks. One main concern about the semiring parsing system is the efficiency considerations. A packed representation for all possible target structures was discussed and different heuristic search strategies have been explored. By investigating more structured probabilistic models, we found that all the models are using the similar packed structures and apply the similar dynamic programming as classic inside-outside algorithms to the parameter estimation, which indicates that semiring parsing can be further extended to more complex models and can integrate more tasks, such as probabilistic learning. Semiring parsing turns out to have a solid theoretical foundation and has a promising perspective of applications.