Plate notation

In Bayesian inference, plate notation is a method of representing variables that repeat in a graphical model.

[2] 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

The M in the corner of the plate indicates that the variables inside are repeated M times, once for each document.

The circle representing the individual words is shaded, indicating that each

A number of extensions have been created by various authors to express more information than simply the conditional relationships.

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.

The diagram on the right shows a few more non-standard conventions used in some articles in Wikipedia (e.g. variational Bayes): Plate notation has been implemented in various TeX/LaTeX drawing packages, but also as part of graphical user interfaces to Bayesian statistics programs such as BUGS and BayesiaLab and PyMC.

Plate notation for Latent Dirichlet allocation
Bayesian multivariate Gaussian mixture model using plate notation. Smaller squares indicate fixed parameters; larger circles indicate random variables. Filled-in shapes indicate known values. The indication [K] means a vector of size K ; [D,D] means a matrix of size D × D ; K alone means a categorical variable with K outcomes. The squiggly line coming from z ending in a crossbar indicates a switch — the value of this variable selects, for the other incoming variables, which value to use out of the size- K array of possible values.