Model of Vietnamese associative grammar

3.3.1.2. Training Algorithm

As discussed in Chapter 1 with a context-free grammar, probabilities acting as parameters can initially be generated at random, and then updated every time a new sentence is analyzed and added to the set. corpus. The training algorithm proposed by [79] aims to recalculate the parameter value after processing the input sentence. Like the context-free grammar, this algorithm relies on two parameters, the inner probability and the outer probability.

The probability in PrI ( L, R, l, r ) is the probability that words from L to R can be linked together such that the connections l and r are satisfied.

The outer probability Pro ( L, R, l, r ) is the probability that words outside the range L to R can be associated with each other such that the outer join requirements l and r are satisfied.

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The inner probability is calculated recursively according to the relations:

According to the parsing algorithm in Figure 3.4, it is clear that PI ( wi , wi+1, NIL, NIL ) = 1 with 0 ≤ i ≤ n-1.

For example , with the linking grammar and the sentence “ I bought a flower ” mentioned above,

PrI ( 1, 4, NIL, NcNt3 ) = Pr (3, (McN)(NcNt3),→ | 1, 4, NIL, NcNt3 ) × PrI ( 1, 3, NIL, McN ) × PrI ( 3, 4
, NIL, NIL )

with the values of the probabilities given in (3.1) :

PrI( 1, 3, NIL, McN) = Pr(2, ( )(McN), → | 1, 3, NIL, McN) × PrI (1, 2, NIL,NIL) × PrI (2, 3,
NIL , NIL)
= 0.06 × 1 × 1 = 0.06
Pr ( 3, (McN)(NcNt3),→ | 1, 4, NIL, NcNt3 ) = 0.05

so, PrI (buy, flower, NIL, NcNt3) = 0.05 × 0.06 = 0.003 (3.5)

The probabilities outside PrO are calculated recursively: initially, for each d ∈ D(W0) there is left[d] = NIL, set

The probability is added up for the 4 possible cases in the previous step (then R and L also play the role of W):

Figure 3.22 . Describe how to calculate probability Pr0 ⊲left(L, W, l ⊳, ⊲ left[D])

According to [79], Counts are calculated in the following formulas (3.6) to (3.9) :

The value of count(L, R, l, r) is calculated in the analysis algorithm:

where δ is a function that takes the value 1 if l = NIL, 0 otherwise, match takes the value 1 if the two matches match, 0 otherwise. Notice match(c,NIL) = match(NIL,c) = 0.

The Pr(S) value stated in the above formulas is calculated according to the following formula:

The values Count(L, R, l, r), Count(W, l, r) and Count(d, l, r) are calculated directly according to the connections and selections that appear in the corpus.

Model of Vietnamese associative grammar - 21

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