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

CHAPTER 5. PROBABILISTIC ATTRIBUTE GRAMMARS 115feature equations lead to unnecessary splitting of feature probabilities, and are thus already disfavored by thelikelihood component of the posterior probability.5.4 Experiments5.4.1 * 0 examplesAs mentioned in the introduction (Chapter 1), the motivation for the PAG extension to SCFGs camepartly from the ¨ 0 miniature language learning task proposed by Feldman et al. (1990). It was thereforenatural to test the formalism on this problem. No description length bias on feature equations was used.A minimal ¨ 0 fragment for English and the associated generating grammar was already presentedas the example grammar in Section 5.2.2. A version of this grammar with 3 nouns, 2 prepositions, and 2 verbsof each category was used to generate a random 100-sentence sample. All alternative productions were givenequal probability. The generated sentences were then processed by incremental best-first search using theinduction operators described above.The result grammar found is weakly equivalent to the target.This includes accurate featureattributions to the various terminal symbols, as well as appropriate feature-passing to instantiate the top-levelfeatures. The only structural difference between the two grammars was a flatter phrase structure for theinduced grammar: 5S --> NP ViS.tr = NP.fS.rel = Vi.h--> NP Vc P NPS.tr = NP(1).fS.lm = NP(2).f--> NP Vt NPS.tr = NP(1).fS.lm = NP(2).fS.rel = Vt.hNP --> Det NNP.f = N.fThe lexical productions and feature assignments for N, P, Vi, Vt, Vt, and Det are as in the example grammar.As for the base SCFG case (discussed in Section 4.5.2), a beam search finds a deeper phrase structurewith a somewhat higher posterior probability:S --> NP VPS.tr = NP.fS.lm = VP.gS.rel = VP.hVP --> Vi5 As usual we rename the arbitrary nonterminal and feature names generated by the implementation to be close to the target grammar,to make the result more intelligible.