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

$D(ℓ1,ℓ2)$ 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 $βi(r,ℓ)$, indicating a scalar prior to a specific node i or an untranslated word type.

β(i,) A symmetric Dirichlet prior vector of size $Vi(ℓ)$, where $Vi(ℓ)$ 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

$D(ℓ1,ℓ2)$ 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 $βi(r,ℓ)$, indicating a scalar prior to a specific node i or an untranslated word type.

β(i,) A symmetric Dirichlet prior vector of size $Vi(ℓ)$, where $Vi(ℓ)$ 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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