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

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CHAPTER 4. STOCHASTIC CONTEXT-FREE GRAMMARS 964.5.2 Natural language syntaxIn this section we show examples of applying the Bayesian SCFG merging algorithm to simpleexamples of natural language syntax. A strong caveat is in order at this point: these experiments do notinvolve actual natural corpus data. Instead, they make use of artificial corpora generated from grammars thatare supposed to model various aspects of natural languages in idealized form, and subject to the inherentconstraints of context-free grammars.The main goal in these experiments will be to test the ability of the algorithm to recover specifictypical grammatical structures from purely distributional evidence (the stochastically generated corpora).Applying the algorithm to actual data involves additional problems that will be discussed towards the end.As indicated in Section 4.3.4, we used a prior for production lengths corresponding to a Poissondistribution. The prior mean for the length was set to 3.0.Lexical categories and constituencyThe following grammar will serve as a baseline for the followingexperiments. It generates simple sentences based on transitive and intransitive verbs, as well as predicationsinvolving prepositional phrases. Unless otherwise indicated, all productions for a given LHS have equalprobability.S --> NP VPNP --> Det NVP --> Vt NP--> Vc PP--> ViPP --> P NPDet --> a--> theVt --> touches--> coversVc --> isVi --> rolls--> bouncesN --> circle--> square--> triangleP --> above--> belowThe corresponding corpus contains 100 randomly generated sentences, including repetitions. (Thetotal number of distinct sentences generated by the grammar is 156.) The following samples illustrate therange of allowed constructions:the circle covers a squarea square is above the trianglea circle bouncesThe corpus was given as input to incremental, best-first merging. The algorithm produced theeventual result grammar after having processed the first 15 samples from the corpus.
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.
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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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Consider the following problem: sta
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CHAPTER 8. FUTURE DIRECTIONS 1828.2
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184BibliographyAHO, ALFRED V., RAVI
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BIBLIOGRAPHY 186DAGAN, IDO, FERNAND
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BIBLIOGRAPHY 188——, & ——. 1
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BIBLIOGRAPHY 190QUINLAN, J. ROSS, &
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BIBLIOGRAPHY 192WALLACE, C. S., & P
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