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

CHAPTER 5. PROBABILISTIC ATTRIBUTE GRAMMARS 108VP.g = PP.gVP.h = PP.h--> Vt NPVP.g = NP.fVP.h = Vt.hDet --> aN--> circleN.f = ‘circle’--> squareN.f = ‘square’...Vc --> isVi --> movesVi.h = ‘move’--> fallsVi.h = ‘fall’Vt --> touchesVt.h = ‘touch’--> coversVt.h = ‘cover’...PP --> P NPPP.g = NP.fPP.h = P.hP --> aboveP.h = ‘above’--> belowP.h = ‘below’...All feature names except for the top-level ones can be chosen arbitrarily. In particular, there is no requirementthat the LHS feature names coincide with RHS feature names, although this is often convenient to make thefeature equations more readable.Simple lexical ambiguities can be modeled using feature assignments with non-unit probabilities,e.g., for the nonsense word squangle:N --> squangleN.f = ‘square’ [0.5]N.f = ‘triangle’ [0.5]5.2.3 PAG estimationSince PAGs are not a standard grammar formalism there is no standard estimation algorithm that setsthe PAG probability parameters given a set of samples and grammar rules. However, an iterative likelihoodmaximization scheme based on EM techniques can be applied here as well.Since our focus here is on merging (i.e., structure learning), rather than parameter estimationapproaches, we will not give the details of this algorithm here. The basic idea is to estimate the SCFG part ofthe grammar separately, and then, for a given SCFG derivation to compute the co-occurrence of feature values