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

CHAPTER 5. PROBABILISTIC ATTRIBUTE GRAMMARS 120cannot be adequately described, let alone learned. 8The obvious solution to this representational problem are hierarchical feature structures (f-structures)as used by a number of linguistic theories of grammar (Shieber 1986). However, this raises new problemsconcerning the ‘proper’ probabilistic formulation. For example, the set of hierarchical feature specificationsover a finite set of feature names becomes infinite, raising the question of an appropriate prior distributionover this space. Also, new and more varied merging operators would have to be introduced to match theincreased expressiveness of the formalism, leading to new intricacies for the search procedure. Still, pursuingsuch an extension, maybe not in the full generality of standard f-structures, is a worthwhile subject for futureresearch.5.5.3 Trade-offs between context-free and feature descriptionsReturning to the issue of generalized feature constraints,there is also a fundamental question on whatevidence such ‘hidden’ feature constraints could be learned. We have seen in Section 4.5.2 that agreement,for example, can be represented and learned based on posterior probabilities and merging operators, but itbecame clear that context-free productions are an inadequate formalism for these phenomena. Ideally, onewould want to move from a description such astoS --> NP_sg VP_sg--> NP_pl VP_plS --> NP VPNP.number = VP.numberIn general, there are other cases where context-free rules and features provide alternative models for the samedistributional facts. In such cases a description length criterion should be used to decide which is the betterformulation.Incidentally, nonterminals themselves may be expressed as features (Gazdar et al. 1985; Shieber1986), thereby eliminating the need for separate descriptions mechanisms. This could be the basis of a unifieddescription length metric that allows fair comparisons of alternative modeling solutions.5.6 SummaryIn this chapter we examined a minimal extension of stochastic context-free grammars that incorporatessimple probabilistic attributes (or features). We saw how a pair of feature-oriented operators (featuremerging and attribution) together with the existing SCFG operators can induce simple grammars in thisformalism, and applied the approach to a rudimentary form of semantics found in the ¨ 0 miniature language8 A restricted version in which embedding is restricted to one level and the semantics are flattened out in several features can belearned using the operators described in this chapter.