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

CHAPTER 4. STOCHASTIC CONTEXT-FREE GRAMMARS 97The result grammar is weakly equivalent to (generates the same sentence as) the target, and hasidentical lexical rules. However, the sentence-level productions are less structured: 13S --> NP VC P NP (28)--> NP VI (39)--> NP VT NP (33)NP --> DET N (161)The algorithm was thus successful in grouping terminals into appropriate lexical categories and identifyingthe pervasive NP constituents. The log posterior probability of this grammar (-230.30769) is slightly belowthat of the target grammar (-230.1136).phrase structure:However, a more extensive beam-search (width 30) finds an alternative grammar exhibiting a deeperS --> NP VP (100)VP --> VI (39)--> X NP (61)X --> VT (33)--> VC P (28)NP --> DET N (161)This structure turns out to have a somewhat higher log posterior probability than the target (-228.658).Chunking (VC P) is prefered to the standard (P NP) because it allows merging the two VP expansionsinvolving VC and VT, respectively.Interestingly, the importance of the prior distributionfor the production lengths is already evident inthis experiment. Were it not for the Poisson prior length distribution, the flat productions in the first grammarabove would actually yield a higher posterior probability than the target grammar.Recursive embedding of constituentsTo get PP constituents based only on distributional evidence, thegrammar can be enriched, e.g., with topicalized PPs and PPs embedded in NPs. The changed productions areS --> NP VP [3/5]--> PP COMMA NP Vi [1/5]--> PP Vc NP [1/5]NP --> Det N [3/4]--> Det N PP [1/4]COMMA --> ,This extends the range of sentence to samples such asabove a square is the squarethe circle below the triangle below a circle touches the triangleabove a triangle , a circle rollsbelow a square , the triangle above the square below the square bounces13 Induced grammars in this section are notated with nonterminal labels that chosen from the target grammar where possible, so as toenhance readability. The actual nonterminal names are of course irrelevant to the algorithm.