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Table 1 
Notation table.
NotationsDescriptions
z The topic assignment to a token. 
 
w() A word type in language
 
V() The size of vocabulary in language
 
D() The size of corpus in language
 
D(1,2) The number of document pairs in languages 1 and 2
 
α A symmetric Dirichlet prior vector of size K, where K is the number of topics, and each cell is denoted as αk
 
θd, Multinomial distribution over topics for a document d in language
 
β() A symmetric Dirichlet prior vector of size V(), where V() is the size of vocabulary in language
 
β(r,) An asymmetric Dirichlet prior vector of size I + V(,−), where I is the number of internal nodes in a Dirichlet tree, and V(,−) the number of untranslated words in language . Each cell is denoted as βi(r,), indicating a scalar prior to a specific node i or an untranslated word type. 
 
β(i,) A symmetric Dirichlet prior vector of size Vi(), where Vi() is the number of word types in language under internal node i
 
ϕ(,k) Multinomial distribution over word types in language of topic k for topic k
 
ϕ(r,,k) Multinomial distribution over internal nodes in a Dirichlet tree for topic k
 
ϕ(i,,k) Multinomial distribution over all word types in language under internal node i for topic k
NotationsDescriptions
z The topic assignment to a token. 
 
w() A word type in language
 
V() The size of vocabulary in language
 
D() The size of corpus in language
 
D(1,2) The number of document pairs in languages 1 and 2
 
α A symmetric Dirichlet prior vector of size K, where K is the number of topics, and each cell is denoted as αk
 
θd, Multinomial distribution over topics for a document d in language
 
β() A symmetric Dirichlet prior vector of size V(), where V() is the size of vocabulary in language
 
β(r,) An asymmetric Dirichlet prior vector of size I + V(,−), where I is the number of internal nodes in a Dirichlet tree, and V(,−) the number of untranslated words in language . Each cell is denoted as βi(r,), indicating a scalar prior to a specific node i or an untranslated word type. 
 
β(i,) A symmetric Dirichlet prior vector of size Vi(), where Vi() is the number of word types in language under internal node i
 
ϕ(,k) Multinomial distribution over word types in language of topic k for topic k
 
ϕ(r,,k) Multinomial distribution over internal nodes in a Dirichlet tree for topic k
 
ϕ(i,,k) Multinomial distribution over all word types in language under internal node i for topic k
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