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

CHAPTER 5. PROBABILISTIC ATTRIBUTE GRAMMARS 118The result is that probabilities have to be split (the exact probabilities depend on the sample statistics), therebylowering the grammar likelihood. This alternative syntactic structure is therefore less preferable than the first,but only due to the attached semantic features.5.5 Limitations and ExtensionsThe PAG framework as introduced in this chapter has a number of more or less obvious shortcomings,mainly as a result of our desire to keep the probabilistic model simple enough so that various techniquesfamiliar from earlier models could be used (combinations of multinomials with associated priors, Viterbiapproximations, simple merging operators, etc.) Below we mention the most important limitations andpossible extensions to remedy them.5.5.1 More expressive feature constraintsDerivation probabilities for PAGs were defined with carefully chosen conditional independencestipulations in order to make them computationally tractable.The marginal probability of the context-free aspect of a derivation, –EÃù6 W ±?r+9,–Ã NP VPNP.number = VP.numberNP --> Det NNP.number = N.numberVP --> V NOVP.number = V.number...where number is assigned in the lexical productions for both N and V. Although the feature equation inthe first production is highly intuitive, it would effectively require stating a marginal probability for the jointevent of value assignments, as opposed to conditional probabilitiy of one value given the other. However, the6 Therefore the strict bottom-up feature format could be relaxed, e.g., by using the notion of L-attributed feature specifications (Ahoet al. 1986).