PCFG based approaches are desired to be scalable and general enough. Compromising speed for accuracy needs to as minimal as possible. Pfold addresses the limitations of the KH-99 algorithm with respect to scalability, gaps, speed and accuracy.

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Definition 1 (PCFGs) A PCFG consists of: 1. A context-free grammarG = (N,Σ,S,R). 2. A parameter q(α → β) for each rule α → β ∈ R. The parameter q(α → β) can be interpreted as the conditional probabilty of choosing rule α → β in a left-most derivation, given that the non-terminal being expanded isα. For any X ∈ N, we have ...

•PCFG is a worse language model for English than n‐gram models •Certain biases: smaller trees more probable (average WSJ sentence 23 words) Slide based on “Foundations of Statistical Natural Language Processing”by Christopher Manning and HinrichSchütze

2020年5月6日 · Probabilistic Context Free Grammar (PCFG) is an extension of Context Free Grammar (CFG) with a probability for each production rule. Ambiguity is the reason why we are using probabilistic version of CFG.

source code of NAACL2021 "PCFGs Can Do Better: Inducing Probabilistic Context-Free Grammars with Many Symbols“ and ACL2021 main conference "Neural Bilexicalized PCFG Induction&...

Learning the parameters of a PCFG If we have a treebank (a corpus in which each sentence is associated with a parse tree), we can just count the number of times each rule appears, e.g.: S ! NP VP . (count = 1000) S ! S conj S . (count = 220) and then we divide the observed frequency of each rule X → Y Z by the sum of the frequencies of all rules

Columbia University - Natural Language ProcessingWeek 3 - Probabilistic Context-Free Grammars (PCFGs)7 - 2 Basics of PCFGs (Part 1)

A PCFG consists of a start state and a set of productions with probabilities. The set of terminals and nonterminals is implicitly specified by the productions. PCFG productions use the ProbabilisticProduction class.

(PCFGs) as a model for statistical parsing. We introduced the basic PCFG for-malism; described how the parameters of a PCFG can be estimated from a set of training examples (a “treebank”); and derived a dynamic pro gramming algorithm for parsing with a PCFG. Unfortunately, the basic PCFGs we have described turn out to be a rather poor