SCFG

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-- associate probability p to each rule and each lexical entry

- restriction for context-free grammar: binary rules: Ap -> Aq Ar matrix Bpqr

unary rules : Ap -> BM matrix Upm

= CHOMSKY NORMAL FORM (CNF)

-- assign a p to each left-most derivation or parse tree, allowed by the underlying CFG

argmax p(t) is the most likely parse tree

- How to obtain PCFG from a treebank?

prob of a sentence: sum of p(t) for all t in T, best parse is max prob from all p(t)

PROS: some idea of the probability of a parse (but not very good),

can be learned without negative examples

provides language model for a language

CONS: provides worse language model than a 3-gram

-- robust, we can combing SCFG with 3-grams

-- assigns a lot of probabilities to short sentences, small trees are more probable

-- parameter estimation (probabliities)

-- problem of sparseness, volume

-- asociation to the rule, information about the point of application of the rule in the derivation tree lost

-- low frequency constructions are penalized

-- probab of a derivation, contextual independence is assumed (CF grammar, but also prob assigment)

-- the possibility of relax conditional independence -> sensitivity to structure, lexicalization

-- node expansion depends on its position in the tree

-- 2 models

Condition/Discriminative model: probability of parse tree directly estimated

probs are conditioned on a concrete sentence

no sentence distrib probs are assumed

sum of all probs is 1

Generative/Joined model

assigns probs to all the trees generated by the grammar

sum of all probs is 1

Probability of a sentence is the sum of the probabilities of all the valid parse trees of the sentence

prob of a subtree is independent of its position in the derivation tree -- positional invariance -- context-free, independence from ancestors

MLE - Maximum Likelihood Estimation - e.g. TreeBank Grammars

P(A -> a) = number of (A-> a) / sum(all rules A-> a in the grammar)

	Created by Doria Šarić over 6 years ago

Note on Probabilistic parsing, created by Doria Šarić on 06/06/2018.

Probabilistic parsing