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

values in the RHSs of productions and feature equations, respectively. Specifically, the operation fattrib , )g?is0CHAPTER 5. PROBABILISTIC ATTRIBUTE GRAMMARS 113N --> square [0.5]N1.f = ‘square’ [1.0]--> circle [0.5]N1.f = ‘square’ [1.0]which preserves the likelihood of the original grammar.The general strategy in combining feature operations with syntactic merging steps is to preservedeterminism in the feature equations where possible, under the constraint that all previouslygenerated samplescan still be generated. The algorithm implementing this strategy has a striking similarity with standard featureunification. Thus, we can think of the feature operations in the example (1) as unifying a constant with thenewly created feature f2, and (2) as unifying the features f1 and f2. Unlike standard unification we canresolve feature value conflicts by splitting probabilities.Feature attribution Although the above method can efficiently find many feature attributions, featureattributions must still be considered independently as potential search steps. A good heuristic to suggestpromising candidates is correlation (or mutual information) between occurrences of nonterminals and featureis considered if )nonterminalpositive mutual information).and feature valueihave close to perfect correlation (or alternatively, largeWhen applying an operator of type fattrib , )g?is0 one has to deal with the nondeterminism arisingfrom multiple occurrences of ) nonterminals in production RHSs. (Which instance ) of should valuei thebe attributed to?) A full search of all alternative attributions would discover that some yield feature mergingopportunities that preserve the model likelihood, while others do not, and chose the appropriate alternativeon that basis.When processing samples in incremental mode a simple, but effective approach is to delay (buffer)processing of those samples which lead to productions that give rise to ambiguity in the feature attributions.Specifically, by first processing samples with distinct feature values, attributionscan be done deterministically.The ambiguities in the held-back samples are then implicitly resolved by merging with existing productions.For example,S --> A CIRCLE IS BELOW A SQUARES.tr = ‘circle’S.lm = ‘square’S.rel = ‘below’S --> A CIRCLE IS BELOW A CIRCLES.tr = ‘circle’S.lm = ‘circle’S.rel = ‘below’The operations fattrib(CIRCLE, circle) is unambiguous for the first production, but not for the second one.The second production is therefore set aside, whereas the first one eventually (after several attribution steps)results in