The dissertation of Andreas Stolcke is approved: University of ...

CHAPTER 6. EFFICIENT PARSING WITH STOCHASTIC CONTEXT-FREE GRAMMARS 165Full CNFSparse CFGBottom-up Inside/outside Stochastic RTNs(Baker 1979) (Kupiec 1992a)Left-to-right LRI Probabilistic(Jelinek & Lafferty 1991) EarleyTable 6.4: Tentative typology of SCFG algorithms according to prevailing directionality and sparseness ofthe CFG.zero. It appears that these algorithms tend to be more naturally formulated in terms of a stochastic process,as opposed to static specifications of string probabilities.To illustrate these points, the algorithms discussed in this section have been arranged in the griddepicted in Table 6.4.6.8 SummaryWe have presented an Earley-based parser for stochastic context-free grammars that is appealing forits combination of advantages over existing methods. Earley’s control structure makes it run with best-knowncomplexity on a number of special grammar classes, and no worse than standard bottom-up probabilistic chartparsers on fully parameterized SCFGs.Unlike bottom-up parsers it also computes accurate prefix probabilities incrementally while scanningits input, along with the usual substring (inside) probabilities. The chart constructed during parsing supportsboth Viterbi parse extraction and Baum-Welch type rule probability estimation by way of a backward passover the parser chart. If the input comes with (partial) bracketing to indicate phrase structure this informationcan be easily incorporated to restrict the allowable parses. A simple extension of the Earley chart allowsfinding partial parses of ungrammatical input.The computation of probabilities is conceptually simple, and follows directly Earley’s parsingframework, while drawing heavily on the analogy to finite-state language models. It does not require rewritingthe grammar into normal form. Thus, the present algorithm fills a gap in the existing array of algorithms forSCFGs, efficiently combining the functionalities and advantages of several previous approaches.6.9 Appendix: LR item probabilities as conditional forward probabilitiesIn Section 6.7.3 an interpretation of LR item probabilities as defined in Wright (1990:Section 2.1)was given in terms of the forward probabilities used by the Earley parser. Below we give a proof for thecorrectness of this interpretation. Notice that these are the ‘ideal’ LR probabilities that should be attached toitems, if it weren’t for the identification of items with close probabilities to keep the LR state list finite.