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PROBABILISTIC CFGs & PROBABILISTIC PARSING. Universita’ di Venezia 3 Ottobre 2003. Probabilistic CFGs. Context-Free Grammar Rules are of the form: S  NP VP In a Probabilistic CFG, we assign a probability to these rules: S  NP VP, P(SNP,VP|S). Why PCFGs?.

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PROBABILISTIC CFGs & PROBABILISTIC PARSING

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PROBABILISTIC CFGs &PROBABILISTIC PARSING

Universita’ di Venezia

3 Ottobre 2003


Probabilistic CFGs

  • Context-Free Grammar Rules are of the form:

    • S  NP VP

  • In a Probabilistic CFG, we assign a probability to these rules:

    • S  NP VP, P(SNP,VP|S)


Why PCFGs?

DISAMBIGUATION: with a PCFG, probabilities can be used to choose the most likely parse

ROBUSTNESS: rather than excluding things, a PCFG may assign them a very low probability

LEARNING: CFGs cannot be learned from positive data only


An example of PCFG


PCFGs in Prolog (courtesy Doug Arnold)

s(P0, [s,NP,VP] ) --> np(P1,NP),vp(P2,VP),{ P0 is 1.0*P1*P2 }.

….vp(P0, [vp,V,NP] ) -->v(P1,V),np(P2,NP ),{ P0 is 0.7*P1*P2 }.


Notation and assumptions


Independence assumptions

PCFGs specify a language model, just like n-grams

We need however to make some independence assumptions yet again: the probability of a subtree is independent of:


The language model defined by PCFGs


Using PCFGs to disambiguate: “Astronomers saw stars with ears”


A second parse


Choosing among the parses, and the sentence’s probability


Parsing with PCFGs:A comparison with HMMs

An HMM defines a REGULAR GRAMMAR:


Parsing with CFGs: A comparison with HMMs


Inside and outside probabilities(cfr. forward and backward probabilities for HMMs)


Parsing with probabilistic CFGs


The algorithm


Example


Initialization


Example


Example


Learning the probabilities: the Treebank


Learning probabilities

Reconstruct the rules used in the analysis of the Treebank

Estimate probabilities by:P(AB) = C(AB) / C(A)


Probabilistic lexicalised PCFGs(Collins, 1997; Charniak, 2000)


Parsing evaluation


Performance of current parsers


Readings

  • Manning and Schütze, chapters 11 and 12


Acknowledgments

  • Some slides and the Prolog code are borrowed from Doug Arnold

  • Thanks also to Chris Manning & Diego Molla


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