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?.

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PROBABILISTIC CFGs & PROBABILISTIC PARSING

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Probabilistic cfgs probabilistic parsing

PROBABILISTIC CFGs &PROBABILISTIC PARSING

Universita’ di Venezia

3 Ottobre 2003


Probabilistic cfgs

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

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

An example of PCFG


Pcfgs in prolog courtesy doug arnold

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

Notation and assumptions


Independence 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

The language model defined by PCFGs


Using pcfgs to disambiguate astronomers saw stars with ears

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


A second parse

A second parse


Choosing among the parses and the sentence s probability

Choosing among the parses, and the sentence’s probability


Parsing with pcfgs a comparison with hmms

Parsing with PCFGs:A comparison with HMMs

An HMM defines a REGULAR GRAMMAR:


Parsing with cfgs a comparison with hmms

Parsing with CFGs: A comparison with HMMs


Inside and outside probabilities cfr forward and backward probabilities for hmms

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


Parsing with probabilistic cfgs

Parsing with probabilistic CFGs


The algorithm

The algorithm


Example

Example


Initialization

Initialization


Example1

Example


Example2

Example


Learning the probabilities the treebank

Learning the probabilities: the Treebank


Learning probabilities

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

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


Parsing evaluation

Parsing evaluation


Performance of current parsers

Performance of current parsers


Readings

Readings

  • Manning and Schütze, chapters 11 and 12


Acknowledgments

Acknowledgments

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

  • Thanks also to Chris Manning & Diego Molla


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