Advanced Database Management System - Tutorials and Notes: How to calculate the probability of a parse tree in PCFG

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Wednesday, 6 May 2020

How to calculate the probability of a parse tree in PCFG

Probabilistic Context Free Grammar How to calculate the probability of a parse tree



Probability of a parse tree:

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We have formally defined PCFG. Now the next question is how to use PCFG to derive the probability of a parse tree (derivation tree). As discussed, a sentence can be parsed into more than one way. That means, we can have more than one parse trees for the sentence as per the CFG due to ambiguity.
Given a parse tree t, with the production rules α1 → β1, α2 → β2, … , αn → βn from R (ie., αi → βi R), we can find the probability of tree t using PCFG as follows;
Equation to calculate probability of a parse tree in PCFG

As per the equation, the probability P(t) of parse tree is the product of probabilities of production rules in the tree t.

Example:
Find the probability of the parse tree t given below;
sample calculation of probability of a parse tree in PCFG
                   = 1.0 * 0.1 * 0.7 * 1.0 * 0.4 * 0.18 * 1.0 * 1.0 * 0.18
                   = 0.0009072
The probability of the parse tree t is calculated as 0.0009072.
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Related links:

How to derive probabilities for production rules from Treebank using maximum likelihood estimate

PCFG probabilities estimation

How to calculated production rule probability in PCFG using tree banks

Probabilistic context free grammar rule probability estimation using tree banks



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