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

CHAPTER 5. PROBABILISTIC ATTRIBUTE GRAMMARS 112After attributing ‘square’ to the new feature SQUARE.f the productions becomeS --> A CIRCLE IS BELOW A SQUARES.tr = ‘circle’S.lm = SQUARE.fS.rel = ‘below’S --> A SQUARE TOUCHES A TRIANGLES.tr = SQUARE.fS.lm = ‘triangle’S.rel = ‘below’SQUARE --> squareSQUARE.f = ‘square’The choice of which feature value to attribute to which nonterminal occurrence on the RHS isnondeterministic, but heuristics can be used in practice (see below).5.3.4 Efficient search for feature operationsCombining operatorsIt is convenient to conceptualize the four operators described above as separateinduction steps. However, in practice is more efficient to combine several of these operators due to theirtypical interactions. In the experiments reported below this was done so the existing two-level best-first searchstrategy could be used, instead of a more extensive search method.The feature attribution and merging operators, in particular, often produce an improved posteriorprobability score in conjunction with certain nonterminal merging operations. Consider the rulesNP --> Det N1 [0.5]NP.f = N1.f1--> Det N2 [0.5]NP.f = ‘circle’N1 --> squareN1.f1 = ‘square’N2 --> circleSimply applying the syntactic merging operation merge(N1, N2) = N would result inNP --> Det N [1.0]NP.f = N.f [0.5]NP.f = ‘circle’ [0.5]N --> square [0.5]N1.f = ‘square’--> circle [0.5]which cuts the probability of all samples using one of these productions in half. Alternatively we might precedethe merging operation by ‘appropriate’ feature operations, namely fattrib(N2, circle) = f2, followed byfmerge(f1, f2) = f. This gives the grammarNP --> Det N [1.0]NP.f = N.f [1.0]