Unsupervised Quality Estimation Model for English to German Translation and Its Application in Extensive Supervised Evaluation

Algorithm 1

The POS alignment algorithm from hypothesis to source sentence based on 𝑛-gram.

Hypothesis  Sentence (POS): 𝑃={𝑝₁,𝑝₂,…,𝑝_𝑚1|𝑚₁∈(1,∞)}

Source  Sentence (POS): 𝑃^𝑠={𝑝^𝑠₁,𝑝^𝑠₂,…,𝑝^𝑠_𝑚2|𝑚₂∈(1,∞)}

∀𝑥∈(1,∞), The Alignment of POS 𝑝_𝑥 in hypothesis:

If    ∀𝑦∈(1,∞): 𝑝_𝑥≠𝑝^𝑠_𝑦 // ∀ means for each, ∃ means there is/are

  𝑝_𝑥→∅; // →shows the alignment

elseif  ∃!𝑦∈(1,∞): 𝑝_𝑥=𝑝^𝑠_𝑦 // ∃! means there exists exactly one

 𝑝_𝑥→𝑝^𝑠_𝑦;

elseif  ∃𝑦₁,𝑦₂∈(1,∞): 𝑝_𝑥=𝑝^𝑠_𝑦1∧𝑝_𝑥=𝑝^𝑠_𝑦2 // ∧ is logical conjunction, and

 foreach  𝑘∈(−𝑛,−1)∪(1,𝑛)

  foreach  𝑗∈(−𝑛,−1)∪(1,𝑛)

   if  ∃𝑘₁,𝑘₂,𝑗₁,𝑗₂: 𝑝_𝑥+𝑘1=𝑝^𝑠_𝑦1+𝑗1∧𝑝_𝑥+𝑘2=𝑝^𝑠_𝑦2+𝑗2

      if  𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑝_𝑥,𝑝^𝑠_𝑦1≤𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑝_𝑥,𝑝^𝑠_𝑦2

        𝑝_𝑥→𝑝^𝑠_𝑦1;

      else

        𝑝_𝑥→𝑝^𝑠_𝑦2;

   elseif  ∃𝑘₁,𝑗₁: 𝑝_𝑥+𝑘1=𝑝^𝑠_𝑦1+𝑗1∧∀𝑘₂,𝑗₂∶𝑝_𝑥+𝑘2≠𝑝^𝑠_𝑦2+𝑗2

    𝑝_𝑥→𝑝^𝑠_𝑦1;

   else  // i.e. ∀𝑘₁,𝑘₂,𝑗₁,𝑗₂: 𝑝_𝑥+𝑘1≠𝑝^𝑠_𝑦1+𝑗1∧𝑝_𝑥+𝑘2≠𝑝^𝑠_𝑦2+𝑗2

     if  𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑝_𝑥,𝑝^𝑠_𝑦1≤𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑝_𝑥,𝑝^𝑠_𝑦2

        𝑝_𝑥→𝑝^𝑠_𝑦1;

     else

        𝑝_𝑥→𝑝^𝑠_𝑦2;

else  // when more than two candidates, the selection steps are similar as above