| Notations . | Descriptions . |
|---|---|
| z | The topic assignment to a token. |
| w(ℓ) | A word type in language ℓ. |
| V(ℓ) | The size of vocabulary in language ℓ. |
| D(ℓ) | The size of corpus in language ℓ. |
| The number of document pairs in languages ℓ1 and ℓ2. | |
| α | A symmetric Dirichlet prior vector of size K, where K is the number of topics, and each cell is denoted as αk. |
| θd,ℓ | Multinomial distribution over topics for a document d in language ℓ. |
| β(ℓ) | A symmetric Dirichlet prior vector of size V(ℓ), where V(ℓ) is the size of vocabulary in language ℓ. |
| β(r,ℓ) | An asymmetric Dirichlet prior vector of size I + V(ℓ,−), where I is the number of internal nodes in a Dirichlet tree, and V(ℓ,−) the number of untranslated words in language ℓ. Each cell is denoted as , indicating a scalar prior to a specific node i or an untranslated word type. |
| β(i,ℓ) | A symmetric Dirichlet prior vector of size , where is the number of word types in language ℓ under internal node i. |
| ϕ(ℓ,k) | Multinomial distribution over word types in language ℓ of topic k for topic k. |
| ϕ(r,ℓ,k) | Multinomial distribution over internal nodes in a Dirichlet tree for topic k. |
| ϕ(i,ℓ,k) | Multinomial distribution over all word types in language ℓ under internal node i for topic k. |
| Notations . | Descriptions . |
|---|---|
| z | The topic assignment to a token. |
| w(ℓ) | A word type in language ℓ. |
| V(ℓ) | The size of vocabulary in language ℓ. |
| D(ℓ) | The size of corpus in language ℓ. |
| The number of document pairs in languages ℓ1 and ℓ2. | |
| α | A symmetric Dirichlet prior vector of size K, where K is the number of topics, and each cell is denoted as αk. |
| θd,ℓ | Multinomial distribution over topics for a document d in language ℓ. |
| β(ℓ) | A symmetric Dirichlet prior vector of size V(ℓ), where V(ℓ) is the size of vocabulary in language ℓ. |
| β(r,ℓ) | An asymmetric Dirichlet prior vector of size I + V(ℓ,−), where I is the number of internal nodes in a Dirichlet tree, and V(ℓ,−) the number of untranslated words in language ℓ. Each cell is denoted as , indicating a scalar prior to a specific node i or an untranslated word type. |
| β(i,ℓ) | A symmetric Dirichlet prior vector of size , where is the number of word types in language ℓ under internal node i. |
| ϕ(ℓ,k) | Multinomial distribution over word types in language ℓ of topic k for topic k. |
| ϕ(r,ℓ,k) | Multinomial distribution over internal nodes in a Dirichlet tree for topic k. |
| ϕ(i,ℓ,k) | Multinomial distribution over all word types in language ℓ under internal node i for topic k. |