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PROBABILISTIC CFGs & PROBABILISTIC PARSING PowerPoint Presentation

PROBABILISTIC CFGs & PROBABILISTIC PARSING

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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(SNP,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

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 }.

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:

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

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)

Learning probabilities

Reconstruct the rules used in the analysis of the Treebank

Estimate probabilities by:P(AB) = C(AB) / C(A)

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

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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