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Incrementally Learning Parameter of Stochastic CFG using Summary Stats. Written by:Brent Heeringa Tim Oates. Goals:. To learn the syntax of utterances Approach : SCFG (Stochastic Context Free Grammar) M=<V,E,R,S> V-finite set of non-terminal E-finite set of terminals

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Incrementally Learning Parameter of Stochastic CFG using Summary Stats

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## Incrementally Learning Parameter of Stochastic CFG using Summary Stats

Written by:Brent Heeringa

Tim Oates

### Goals:

• To learn the syntax of utterances

Approach:

• SCFG (Stochastic Context Free Grammar)

M=<V,E,R,S>

V-finite set of non-terminal

E-finite set of terminals

R-finite set of rules, each r has p(r).

Sum of p(r) of the same left-hand side = 1

S-start symbol

### Problems with most SCFG Learning Algorithms

1)Expensive storage: need to store a corpus of complete sentences

2)Time-consuming: algorithms needs to repeat passes throughout all data

### Learning SCFG

• Inducing context-free structure from corpus(sentences)

• Learning – the production(rules) probabilities

General method: Inside/Outside algorithm

Expectation-Maximization (EM)

Find expectation of rules

Maximize the likelihood given both expectation & corpus

Entire sentence corpus must be stored using some representation(eg. chart parse)

Expensive storage (unrealistic for human agent!)

### Proposed Algorithm

• Use Unique Normal Form (UNF)

• Replace all terminal A-z to 2 new rules

• A->D p[A->D]=p[A->z]

• D-> z p[D->z]=1

• No two productions have the same right hand side

### Learning SCFG- Proposed Algorithm -cont

• Use Histogram

• Each rule has 2 histograms (Hor, HLr)

### Proposed Algorithm -cont

• Hor -contructed when parsing sentences in O

• HLr- -will continue to be updated throughout learning process

• HLr rescale to fixed size h

• Why?!

• Recently used rules has more impact on histogram

• ### Comparing between HLr & Hor

• Relative entropy

• T decrease- increase prob of rules used

• (if s large, increase prob of rules used when parsing last sentence )

• T increase- decrease prob of rules used

(eg pt+1(r)=0.01* p t+1(r)

Inside/Outside

O(n3)

Good

3-5 iterations

Need to store complete sentence corpus

Proposed Algo

O(n3)