In the previous post I attempted to introduce a DSL for probabilistic models inspired by the plate notation. Let’s try to see if we can define LDA with it.

```
> data LDALabels = Alpha | Beta | Topics | Topic
> | Doc | Symbols | Symbol
> lda :: Network LDALabels
> lda =
> [
> Only Alpha :-> Docs
> , Only Beta :-> Symbols
> , (Topics :@ Doc) :-> Topic
> , (Symbols :@ Topic) :-> Symbol
> ]
```

Here is a topic model where topics are arranged in nodes of a fixed binary tree for each document. Let’s say the tree has depth , then the distribution is parameterized by a `TopicPath`

distribution (to select a leaf) and a `TopicDepth`

distribution (to select a node along the path).

```
> data LDATreeLabels =
> Alpha1 | Alpha2 | Beta
> | TopicDepth | TopicPath | Topic | Doc
> | Symbols | Symbol
>
> ldaTree :: Network LDATreeLabels
> ldaTree =
> [
> Only Alpha1 :-> TopicDepth
> , Only Alpha2 :-> TopicPath
> , Only Beta :-> Symbols
> , (TopicPath :@ Doc) :-> Topic
> , (TopicDepth :@ Doc) :-> Topic
> , (Symbols :@ Topic) :-> Symbol
> ]
```

I think it looks pretty good so far. Let’s see how it up once I start interpreting the DSL.