... rewrite a non-terminal as a terminal A → w, and binary pro-ductions rewrite a nonterminal as two nontermi-nals A → BC, where A, B, C ∈ K and w ∈ Wl.The rule probabilities for each nonterminalA ... where K is aset of nonterminals, Wlis a set of terminals, andΦlis a set of rule probabilities. Note that a set ofnonterminals K is shared among languages, buta set of terminals Wland rule ... languages from non-parallelmultilingual corpora in an unsupervisedfashion. For this purpose, we assume agenerative model for multilingual corpora, where each sentence is generated from alanguage...