Plate notation【转】

Plate notation is a method of representing variables that repeat in a graphical model. Instead of drawing each repeated variable individually, a plate or rectangle is used to group variables into a subgraph that repeat together, and a number is drawn on the plate to represent the number of repetitions of the subgraph in the plate.^[1] The assumptions are that the subgraph is duplicated that many times, the variables in the subgraph are indexed by the repetition number, and any links that cross a plate boundary are replicated once for each subgraph repetition.^[2]

[edit]Example

Plate notation for Latent Dirichlet allocation

In this example, we consider Latent Dirichlet allocation, a Bayesian network that models how documents in a corpus are topically related. There are two variables not in any plate; α is the parameter of the uniform Dirichlet prior on the per-document topic distributions, and β is the parameter of the uniform Dirichlet prior on the per-topic word distribution.

The outermost plate represents all the variables related to a specific document, including $θ i$ , the topic distribution for document i. The M in the corner of the plate indicates that the variables inside are repeated M times, once for each document. The inner plate represents the variables associated with each of the $N i$ words in document i: $z i j$ is the topic for the jth word in document i, and $w i j$ is the actual word used.

The N in the corner represents the repetition of the variables in the inner plate $N i$ times, once for each word in document i. The circle representing the individual words is shaded, indicating that each $w i j$ is observable, and the other circles are empty, indicating that the other variables are latent variables. The directed edges between variables indicate dependencies between the variables: for example, each $w i j$ depends on $z i j$ and β.

[edit]References

^ Ghahramani, Zoubin (2007/08). Graphical models (Speech). Tübingen, Germany. Retrieved 2008-02-21.
^ Buntine, Wray L. (December 1994). "Operations for Learning with Graphical Models" (PDF). Journal of Artificial Intelligence Research (AI Access Foundation) 2: 159–225. ISSN 11076-9757. Retrieved 2008-02-21.