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Polynomial Tree Substitution Grammars: Characterization and New Examples
"... Polynomial Tree Substitution Grammars, a subclass of STSGs for which finding the most probable parse is no longer NPhard but polynomial, are defined and characterized in terms of general properties on the elementary trees of the grammar. Necessary and sufficient conditions for effective polynomi ..."
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Polynomial Tree Substitution Grammars, a subclass of STSGs for which finding the most probable parse is no longer NPhard but polynomial, are defined and characterized in terms of general properties on the elementary trees of the grammar. Necessary and sufficient conditions for effective polynomiality are first given. Then, various sufficient properties which are easier to compute are analyzed. The minmax selection principle is shown to be one such sufficient property. Another instance of sufficient properties, based on lexical heads, is also presented. The performances of both models are evaluated on several corpora.
Chapter 1 Polynomial Tree Substitution Grammars: Characterization and New Examples
"... ABSTRACT. Polynomial Tree Substitution Grammars, a subclass of STSGs for which finding the most probable parse is no longer NPhard but polynomial, are defined and characterized in terms of general properties on the elementary trees of the grammar. Necessary and sufficient conditions for effective p ..."
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ABSTRACT. Polynomial Tree Substitution Grammars, a subclass of STSGs for which finding the most probable parse is no longer NPhard but polynomial, are defined and characterized in terms of general properties on the elementary trees of the grammar. Necessary and sufficient conditions for effective polynomiality are first given. Then, various sufficient properties which are easier to compute are analyzed. The minmax selection principle is shown to be one such sufficient property. Another instance of sufficient properties, based on lexical heads, is also presented. The performances of both models are evaluated on several corpora. 1.1 Motivations Stochastic Tree Substitution Grammars (STSG), mainly used in the DataOriented Parsing (DOP) framework (Bod 1998), are grammars the rules of which consist of syntactic trees, called “elementary trees”. These elementary trees are combined 1 with the substitution operator 2 to give derivations of complete parse trees. In addition, a probability p(t) is assigned to each elementary tree t of the grammar 3. Although TSGs are equivalent to Context FreeGrammars (CFG) from a structural point of view 4, STSGs bring a clear advantage over SCFGs at the probabilistic level. Indeed, STSGs can capture a much larger set of probabilistic dependencies than SCFGs, where probabilities are restricted to contextfree (CF) rules only; i.e. to depth1 elementary trees. However, STSGs suffer from a major drawback: finding the most probable parse tree (MPP) has been proved to be an NPhard problem in the most general case (Sima’an 1996). Various approximated MPP search algorithms have then been developed (Bod 1992; Goodman 1996; Chappelier and Rajman 2000). However, another alternative, first introduced by Chappelier and Rajman (2001), is possible. This approach consists in choosing a set of elementary trees for the STSG in such 1 leftmost first 2 denoted in this paper by “◦”
Chapter 11 Gibbsian Tree Substitution Grammars A discriminant probabilistic model for TSGs.
"... ABSTRACT. Standard stochastic grammars use generative probabilistic models, focusssing on rewriting probabilities conditioned by the symbol to be rewritten. Such grammars therefore tend to give penalty to longer derivations of the same input, which could be a drawback when they are used for analysis ..."
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ABSTRACT. Standard stochastic grammars use generative probabilistic models, focusssing on rewriting probabilities conditioned by the symbol to be rewritten. Such grammars therefore tend to give penalty to longer derivations of the same input, which could be a drawback when they are used for analysis (e.g. parsing, language modelling for speech recognition). In this contribution, we propose a novel nongenerative probabilistic model of TSGs, where probabilities are conditioned by the leaves (i.e. the input symbols) rather than by the root of the parse tree. Several experiments with this new model are presented. 11.1 Motivations Standard stochastic grammars use generative probabilistic models, in which rule probabilities are conditioned by the root symbols of the rules. For instance, the probabilities in Stochastic ContextFree Grammars (SCFGs) actually represent the probabilities of the righthand side of each rule knowing the lefthand side (i.e. the root) of the rule. The purpose of this contribution is to address this question in the framework of Stochastic Tree Substitution Grammars (STSGs). STSGs, mainly used in DataOriented Parsing (DOP) (Bod 1998), are grammars in which the rules consist of syntactic trees, called “elementary trees”. These elementary trees are combined1 with the substitution operator to give derivations of complete parse trees. In addition, a probability is assigned to each elementary tree of the grammar. In the standard model this probability represents the probability