# Phrase Table Combination Based on Symmetrization of Word Alignment for Low-Resource Languages
## 3 An Interpolation System Approach
### Highest-Interpolation System Approach (H-ISA)  
Our proposed approach is based on two parts. The first part explores five symmetrizations of word alignment in three sides of the pivot approaches: src-trg, src-pvt, and pvt-trg. This part is named the direct system approach (DSA). The output of the first part is the candidate list of the symmetrization of word alignment. The second part is the phrase table combination using the symmetrization of word alignment that produced the highest BLEU scores. We call this part an interpolation system approach (ISA). The details of DSA and ISA are as follows:  
1. The DSA is a direct translation between source-target languages (src-trg), i.e., Kk-En and Ja-Id; source-pivot languages (src-pvt), i.e., Kk-Ru and Ja-Ms; and pivot-target languages (pvt-trg), i.e., Ru-En and Ms-Id, for Kk-En and Ja-Id, respectively. To perform direct translation, we use 3-gram and 5-gram orders as our language model, while we use gdfand, intersection, union, scrotgt, and tgttsortex as symmetrization techniques. The purpose of this DSA is two-fold: first, to explore the performance of the used language models and symmetrization techniques by performing a direct translation for the low-resource language pairs; second, to find symmetrization techniques that generate the highest BLEU scores for each of src-trg, src-pvt, and pvt-trg in Kk-En and Ja-Id. Then, we use those symmetrization techniques in our ISA. 2. The ISA is our proposed approach that combines the phrase tables of src-trg, src-pvt, and pvt-trg of Kk-En and Ja-Id. In this ISA, we construct two subsystems: standard-ISA (Std-ISA) and highest-ISA (H-ISA). Std-ISA is our interpolation system that uses gdfand symmetrization technique. H-ISA is our interpolation system that uses the symmetrization technique with the highest BLEU scores from the DSA for each phrase table of src-trg, src-pvt, and pvt-trg. Note that we use a triangulation approach for combining the src-pvt and pvt-trg phrase tables for this ISA as follows:  
* We prune the src-pvt and pvt-trg phrase tables using _filter-pt_[33]. * We then merge the two pruned phrase tables using the triangulation method [34]. We modified the triangulation method [34] for our H-ISA. Given the conditional probabilities of pruned src-pvt (\(p(\vec{s}|\vec{p})^{*}\)) and pvt-trg (\(p(\vec{p}|\vec{t})^{*}\)) phrase tables, we merge the two phrase tables as shown in Equation (3). The two pruned phrase tables were obtained from the DSA of src-pvt and pvt-trg with the highest BLEU scores. \[ \begin{split} p(\vec{s}|\vec{t})^{*}&=\sum_{\vec{p }}p(\vec{s}|\vec{p},\vec{t})^{*}p(\vec{p}|\vec{t})^{*}\\ &\approx\sum_{\vec{p}}p(\vec{s}|\vec{p})^{*}p(\vec{p}|\vec{t})^{* }\end{split} \] (3)
* We merge the triangulation phrase table with the phrase table of src-trg according to Equation (2). We modified Equation (2) for our H-ISA. Given the conditional probabilities of src-trg phrase table (\(p(\vec{s}|\vec{t})^{*}\)) and triangulation phrase table (\(p(\vec{s}|\vec{t})^{*}\)), we merge the two phrase tables as follows: \[ \begin{split} p(s|\vec{t};\lambda)&=\lambda_{\textit{ src-trg}}p(s|\vec{t})^{*}+\lambda_{\textit{ppt}}p(\vec{s}|\vec{t})^{*}\end{split} \] (4) where \(\lambda_{\textit{src-trg}}\) and \(\lambda_{\textit{ppt}}\) are the interpolation weights of the phrase tables, and \(\lambda_{\textit{src-trg}}+\lambda_{\textit{ppt}}=1\). The src-trg phrase table (\(p(s|\vec{t})^{*}\)) was obtained from the DSA of src-trg with the highest BLEU scores. Algorithm 1 shows the strategy of our H-ISA. We use 3-gram and 5-gram orders as our language model in this ISA, as well as in the DSA. We chose 3-gram as the minimum order because it can predict a better probability of the next word than other lower \(n\)-grams, i.e., 2-gram. We used 5-gram as the maximum order because [PERSON] et al. [35] showed that a system using more than 5-gram has relatively thesame BLEU score as 5-gram.