Probabilistic Context-Free Grammar
A Probabilistic Context-Free Grammar is a context free phrase-structure grammar where each production rule is a probabilistic production rule.
- AKA: PCFG, Stochastic Context-Free Grammar, SCFG.
- Context:
- It can be a Lexicalized Probabilistic Context Free Grammar.
- See: Context Free Grammar, PCFG-based Parse Tree, CYK Algorithm.
References
2011
- (Sakakibara, 2011) ⇒ Yasubumi Sakakibara. (2011). "Probabilistic Context-Free Grammars." In: (Sammut & Webb, 2011) p.802
2009
- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Stochastic_context-free_grammar
- A stochastic context-free grammar (SCFG; also probabilistic context-free grammar, PCFG) is a Context-Free Grammar in which each production is augmented with a probability. The probability of a derivation (parse) is then the product of the probabilities of the productions used in that derivation; thus some derivations are more consistent with the stochastic grammar than others.
SCFGs extend context-free grammars in the same way that Hidden Markov Models extend Regular Grammars.
SCFGs have application in areas as diverse as Natural Language Processing to the study of RNA molecules. SCFGs are a specialized form of Weighted Context-Free Grammars.
- A stochastic context-free grammar (SCFG; also probabilistic context-free grammar, PCFG) is a Context-Free Grammar in which each production is augmented with a probability. The probability of a derivation (parse) is then the product of the probabilities of the productions used in that derivation; thus some derivations are more consistent with the stochastic grammar than others.
2007
- (Kakkonen, 2007) ⇒ Tuomo Kakkonen. (2007). "Framework and Resources for Natural Language Evaluation." Academic Dissertation. University of Joensuu.
- In probabilistic grammar formalisms a probability is associated with each rule. For example, probabilistic context-free grammars (PCFGs) can be characterized as CFPSGs that assign to each production the probability of its use. A PCFG (Booth & Thompson 1973) is a 4-tuple G = (N, Σ, P, S) like a CFPSG (Definition 3-9), except that each rule in P is associated with a probability in which α will be expanded to β.
- Definition 3-10. Productions in probabilistic context-free phrase structure grammar.
- 1. P = {a ®b a Î N,b Î(ΣÈN)*}.
- 2. There is a probability function p: P→[0,1] such that for each a ÎN,Σ p(a ®b a )= 1.