# Parsing and understanding plate notation for topic modeling example?

I'm trying to understand the following plate notation which is used a lot as an example of topic model to introduce variational methods, etc.

I wanted to ask if my understanding is correctly depicted in the attempt sketched below in order to parse and unfold the plate notation of the topic model represented?

I have omitted the $$\alpha$$ and $$\theta$$ parameters but please feel free to add them in case it makes the example more understandable and easier for others to read as well.

Thanks!

New diagram describing how to parse plate notation of LDA topic model taking into account @Tracy Chen comments

• So there's no one here who has had the same question or had gone through the same notation before? I just need someone to indicate my mistakes, that's all. Commented Dec 2, 2019 at 12:12

1. Which topic models are you referring to here? If you mean Latent Dirichlet Allocation, please note that your plate diagram is inaccurate, as in LDA we assume each document has its own $$\theta_d$$. For the plate diagram of LDA, please see this paper.
2. Let's assume you are drawing another type of topic model, in your model, the assumption is that the whole corpus shares the same topic proportion $$\theta$$, while in each document, it only contains one topic $$z_d$$. Then you are right about the repetitions of $$z_d$$, however, for each word, you don't need to repeat $$\beta_K$$ for $$K$$ times, as it can only come from one topic distribution ($$\beta_k$$, while $$k=z_d$$ as $$z_d$$ is only an index).
• You're absolutely right, good catch, in that case the hand drawn diagram should be modified in order each $z_{d}$ to get its own $\theta$ and not a shared one as it is represented now? Commented Mar 2, 2020 at 17:51
• The notation should be $\theta_d$, $z_{nd}$, $w_{nd}$, i.e. a document has a $\theta$, each word $w$ has its own topic assignment $z$. (Not each $z_{nd}$ gets its own $\theta$) Commented Mar 2, 2020 at 18:04
• Yes. that's exactly what I meant (if I understand you correctly) instead of having a single vector $\theta_{1,\ldots,K}$ where each element/value $k$ representing all the document $z_{d}$, now each $z_{1\ldots,d}$ gets its own $\theta_{1,\ldots,K}$, where supposedly we have chosen $K=10$ topics, for the sake of the example. Commented Mar 2, 2020 at 18:29