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.

May 6, 2020 · 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.

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

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

May 6, 2017 · Let’s use all these 3595 POS-tagged training trees to learn the PCFG grammar. There are ~10k of lexicon rules producing terminals (with non-zero probabilities ) are learnt, some of them are shown below:

(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

• A probabilistic context-free grammar (PCFG) is a context-free grammar in which ‣ each production rule A → w has a probability P(A → w | A): when we expand A, how likely is it that we choose A → w? ‣ for each nonterminal A, probabilities must sum to one: ‣ we will write P(A → w) instead of P(A → w | A) for short X w

A PCFG G consists of 1. A set of terminals: {wk}, k = 1...,V 2. A set of non terminals: {Ni}, i = 1...,n 3. A designated Start symbol: N1 4. A set of rules: {Ni → ξj}, i = 1...,n 5. A probability function P which assigns probabilities to rules so that, for all nonterminals Ni X j P(Ni → ξj) = 1 Conventions: Notation Meaning G Grammar (PCFG)