For training, we derive growth transformations for phrase and lexicon translation probabilities to iteratively improve the objective.

For effective optimization, we derive updating formulas of growth transformation (GT) for phrase and lexicon translation probabilities .

Then the phrase translation probabilities were estimated based on the phrase alignments.

In the topic-specific lexicon translation model, given a source document, it first calculates the topic-specific translation probability by normalizing the entire lexicon translation table, and then adapts the lexical weights of rules correspondingly.

The process of rule-topic distribution estimation is analogous to the traditional estimation of rule translation probability (Chiang, 2007).

The lexicon translation probability is adapted by:

Such models first estimate word translation probabilities conditioned on topics, and then adapt lexical weights of phrases

o Phd_h7- and Phde- (3|t), translation probabilities for HD—HRs;

Plea, and Plea, (3|t), lexical translation probabilities for HD—HRs;

Ptyhcbhr = escp (—1), rule penalty for HD—HRs; PW (t|s), translation probability for NRRs;