Plate notation

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Plate notation for Latent Dirichlet allocation


The outermost plate represents all the variables related to a specific document, including \theta_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_{ij} is the topic for the jth word in document i, and w_{ij} 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_{ij} 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_{ij} depends on z_{ij} and β.



A number of extensions have been created by various authors to express more information than simply the conditional relationships. However, few of these have become standard. Perhaps the most commonly used extension is to use rectangles in place of circles to indicate non-random variables -- either parameters to be computed, hyperparameters given a fixed value (or computed through empirical Bayes), or variables whose values are computed deterministically from a random variable.




  1. ^ Ghahramani, Zoubin (2007/08). Graphical models (Speech). Tübingen, Germany. Retrieved 2008-02-21.  Check date values in: |date= (help)
  2. ^ Buntine, Wray L. (December 1994). "Operations for Learning with Graphical Models" (PDF). Journal of Artificial Intelligence Research (AI Access Foundation) 2: 159–225. ISSN 1076-9757. Retrieved 2008-02-21.