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CHAPTER 6. EFFICIENT PARSING WITH STOCHASTIC CONTEXT-FREE GRAMMARS 156(a)(b)STATE SET 00 --> .Spredicted ...0 S --> .NP VP0 NP --> .DET NSTATE SET 1scanned "a" ...0 DET --> a .completed ...0 --> DET .MAX 0 DET --> a .0 NP --> DET .Npredicted ...STATE SET 2scanned "circle" ...1 N --> circle .completed ...0 --> NP .1 --> N .MAX 0 NP --> DET N .1 N --> circle .0 S --> NP .VPpredicted ...2 VP --> .VI PP2 VP --> .VT NPSTATE SET 3scanned "touches" ...2 VT --> touches .completed ...2 --> VT .MAX 2 VT --> touches .2 VP --> VT .NPpredicted ...3 PP --> .P NPSTATE SET 0STATE SET 1STATE SET 2STATE SET 30 --> .?0 --> DET .?0 --> NP .?0 --> DET N .?0 --> NP VT .?0 --> DET N VT .?STATE SET 4scanned "below" ...3 P --> below .completed ...3 --> P .MAX 3 P --> below .3 PP --> P .NPpredicted ...4 S --> .NP VP4 NP --> .DET NSTATE SET 5scanned "a" ...4 DET --> a .completed ...4 --> DET .MAX 4 DET --> a .4 NP --> DET .Npredicted ...STATE SET 6scanned "square" ...5 N --> square .completed ...3 --> PP .4 --> NP .MAX 3 PP --> P NP .5 --> N .4 NP --> DET N .5 N --> square .4 S --> NP .VPSTATE SET 4STATE SET 5STATE SET 60 --> NP VT P .?0 --> DET N VT P .?0 --> NP VT P DET .?0 --> DET N VT P DET .?0 --> NP VT PP .?0 --> DET N VT PP .?0 --> NP VT P NP .?0 --> DET N VT P NP .?0 --> NP VT P DET N .?0 --> DET N VT P DET N .?Table 6.3: Robust parsing using the simple grammar from Table 6.1.(a) State sets generated from parsing the ungrammatical string a circle touches above a square.Dummy states (those with empty LHS) represent partial parses. States representing ‘maximal’partial parses are marked with MAX. Predictions that don’t lead to completions have been omittedto save space. (b) Trace of variable state completions resulting in a list of complete partial parsesfor this input.
¸H :6¸.}=Œ£CHAPTER 6. EFFICIENT PARSING WITH STOCHASTIC CONTEXT-FREE GRAMMARS 157left of the dot, and a variable to the right of the dot, written as a question mark:¸As usual, such a state means that the in. nonterminals have generated the substring@A? 16å…å…åindicates that any continuation of the nonterminal sequence is allowed.1. The variableThe variable semantics are taken into account during prediction and completion. A variable stategenerates predictions for all nonterminals, thus having the same effect as the nonterminal-specific dummystates in the previous section. During completion, a variable state combines with all complete states to yieldnew variable states:.—£ ?:6H : d=˜&£? .M£:6?Hfor all=. (That is, the completeŽis inserted before the dot and the variable retained following6QCnonterminal=the dot to allow further completions.) This is implemented by a trivial modification to the standard completionstep. Inner probabilities, Viterbi probabilities and Viterbi back-pointers are processed as usual.¸The net effect of processing variable states is that all complete partial parses can be read off the finalstate set in the chart as the right-hand sides of variable states (after discarding the variable itself). The innerprobability of a variable state reflects the combined likelihood of the partial parse for the given input. TheViterbi probability of a variable state is the joint maximum achieved by the most likely parses for each of thesubstrings. Different derivations from the same complete partial parse may split the input string at differentplaces. The Viterbi-parse procedure when applied to a variable state will recover the most likely such split.Table 6.3(b) shows a trace of variable state completions used in enumerating the partial parses forthe example given earlier.The total number of complete partial parses can be exponential in the length of the input. It maytherefore be desirable to compute only a subset of them, applying some application-specific filter criterion.One such criterion is that one is only interested in ‘maximal’ complete partial parses. A complete partialparse is called maximal if it has no subsequence of nonterminals that can be replaced by another nonterminalso as to yield another complete partial parse. For example, in the case of a circle touches above a square, theonly maximal parse is ‘NP VT PP’.It turns out that a filter for maximal partial parses is easy to implement in the Earley framework.Maximal parses contain only nonterminals that are not themselves part of a larger partial parse. Therefore,during completion, we can mark all states that contributed to a larger constituent, and later identify theunmarked states as the ones corresponding to maximal parses. (The chart in Table 6.3(a) has all maximalstates labeled with MAX.) When completing variable states we simply skip all completions due to non-maximalstates. The list of complete partial parses obtained from the chart will then contain precisely the maximalones.
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The dissertation of Andreas Stolcke
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Bayesian Learning of Probabilistic
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iAcknowledgmentsLife and work in Be
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iiiContentsList of FiguresList of T
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CONTENTSv4.5.4 Summary and Discussi
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CHAPTER 1. INTRODUCTION 2Instance-b
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CHAPTER 1. INTRODUCTION 4A.0.830.33
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CHAPTER 1. INTRODUCTION 6the ¨ 0 l
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CHAPTER 2. FOUNDATIONS 20Global mod
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CHAPTER 3. HIDDEN MARKOV MODELS 74b
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domain. 3 In short, we will leave o
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CHAPTER 4. STOCHASTIC CONTEXT-FREE
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104Chapter 5Probabilistic Attribute
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Page 134 and 135: 122Chapter 6Efficient parsing with
Page 136 and 137: 1z1CHAPTER 6. EFFICIENT PARSING WIT
Page 138 and 139: and each state in set ( -ÏH ):6)
Page 140 and 141: NPDetVTVI P CHAPTER 6. EFFICIENT PA
Page 142 and 143: CHAPTER 6. EFFICIENT PARSING WITH S
Page 144 and 145: ) In particular, the string probabi
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Page 180 and 181: 168Chapter 7-grams from Stochastic
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Page 192 and 193: Consider the following problem: sta
Page 194 and 195: CHAPTER 8. FUTURE DIRECTIONS 1828.2
Page 196 and 197: 184BibliographyAHO, ALFRED V., RAVI
Page 198 and 199: BIBLIOGRAPHY 186DAGAN, IDO, FERNAND
Page 200 and 201: BIBLIOGRAPHY 188——, & ——. 1
Page 202 and 203: BIBLIOGRAPHY 190QUINLAN, J. ROSS, &
Page 204: BIBLIOGRAPHY 192WALLACE, C. S., & P
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