How to calculate the probability of a sentence in NLP using PCFG

Probabilistic Context Free Grammar How to calculate the probability of a sentence given the probabilities of various parse trees in PCFG

Probability of a sentence:

Page 1    Page 2    Page 3

Probability of a sentence is the sum of probabilities of all parse trees that can be derived from the sentence under PCFG;

Example:

Probability of tree t₁

                    = 1.0 * 0.1 * 0.7 * 1.0 * 0.4 * 0.18 * 1.0 * 1.0 * 0.18

                   = 0.0009072

Probability of tree t₂

P(t₂) = 1.0 * 0.1 * 0.3 * 0.7 * 1.0 * 0.18 * 1.0 * 1.0 * 0.18

                    = 0.0006804

Probability of the sentence:

Probability of the sentence “astronomers saw the stars with ears”;

Which is the most probable tree?

The probability of the parse tree t₁ is greater than the probability of parse tree t₂. Hence, t₁ is the more probable of the two parses.

Page 1    Page 2    Page 3

********************

Related links:

• Go to Natural Language Processing (NLP) home

• Go to NLP Solved Exercise page

• Go to Context Free Grammar (CFG) Formal Definition page 
• Go to How to derive production rule probability from Treebank using MLE - Solved exercise page

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