28:. 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. 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.
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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
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Categorical variables that act as "switches", and which pick one or more other random variables to condition on from a large set of such variables (e.g. mixture components), are indicated with a special type of arrow containing a squiggly line and ending in a T
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using plate notation. Smaller squares indicate fixed parameters; larger circles indicate random variables. Filled-in shapes indicate known values. The indication means a vector of size
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are similarly indicated by putting the matrix size in brackets in the middle of the node, with commas separating row size from column size.
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The diagram on the right shows a few more non-standard conventions used in some articles in
Knowledge (XXG) (e.g.
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drawing packages, but also as part of graphical user interfaces to
Bayesian statistics programs such as
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that models how documents in a corpus are topically related. There are two variables not in any plate;
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times, once for each document. The inner plate represents the variables associated with each of the
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The outermost plate represents all the variables related to a specific document, including
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Boldface is consistently used for vector or matrix nodes (but not categorical nodes).
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is the parameter of the uniform
Dirichlet prior on the per-topic word distribution.
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are indicated by placing their size (without a bracket) in the middle of the node.
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are indicated by putting the vector size in brackets in the middle of the node.
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in the corner represents the repetition of the variables in the inner plate
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in the corner of the plate indicates that the variables inside are repeated
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is a method of representing variables that repeat in a
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519:"Operations for Learning with Graphical Models"
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527:Journal of Artificial Intelligence Research
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517:Buntine, Wray L. (December 1994).
492:Ghahramani, Zoubin (August 2007).
170:is the topic distribution for the
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534:. AI Access Foundation: 159–225.
391:ending in a crossbar indicates a
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47:In this example, we consider
430:Variables that are actually
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498:(Speech). TĂĽbingen, Germany
404:parameters to be computed,
90:{\displaystyle \theta _{i}}
49:Latent Dirichlet allocation
42:Latent Dirichlet allocation
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399:array of possible values.
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337:{\displaystyle z_{ij}}
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610:Mathematical notation
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18:Bayesian inference
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577:. Retrieved
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314:depends on
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541:cs/9412102
480:References
470:BayesiaLab
352:Extensions
278:observable
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360:Bayesian
79:θ
61:Dirichlet
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101:. The
32:Example
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