From the tutorial slides: http://mt-class.org/jhu/slides/lecture-tuning.pdf, (slide 37) the powell search algorithm goes as such:
Input: sentences with n-best list of translations, initial parameter values
1: repeat
2: for all parameter do
3: set of threshold points T = {}
4: for all sentence do
5: for all translation do
6: compute line l: parameter value → score
7: end for
8: find line l with steepest descent
9: while find line l2 that intersects with l first do
10: add parameter value at intersection to set of threshold points T
11: l = l2
12: end while
13: end for
14: sort set of threshold points T by parameter value
15: compute score for value before first threshold point
16: for all threshold point t ∈ T do
17: compute score for value after threshold point t
18: if highest do record max score and threshold point t
19: end for
20: if max score is higher than current do update parameter value
21: end for
22: until no changes to parameter values applied
And on slide 31, there's a formula to compute the line l which is used for line 6 of the pseudo code above:
p(ei|f) = λai + bi
However, it's unclear what should the values be for ai and bi.
Given a sentence from the nbest list as such:
0 ||| including options , чтобы buy 20 больше planes , соотношении volume - в том 26 миллиардов долларов . ||| LexicalReordering0= -3.10978 0 0 -6.72232 0 0 Distortion0= 0 LM0= -111.207 WordPenalty0= -18 PhrasePenalty0= 16 TranslationModel0= -13.1426 -8.45991 -12.0762 -11.3076 ||| -746.351
When computing the score for this line for the first parameter of LexicalReordering0, is the p(ei|f) this?:
p(ei|f) = λ*-3.10978 + bi
But what is the value of bi in this case?
Is p(ei|f) = -746.351 for this sentence ?
Does the → score on line 6 of the pseudo code mean -746.351 from the nbest list or does it mean the MT evaluation metric score for this translation with respect to the reference translation (e.g. BLEU)?
What should line 6 of the pseudo code do?
