Plate notation

As explained in Causal AI

Plate notation is a graphical notation that represents repeated variables or subgraphs with enclosing rectangles and repetition indices.

Plate notation represents variables that repeat in a directed acyclic graph (DAG) by enclosing them in rectangles, or plates. A repetition count on each plate preserves dimensional detail without drawing every node individually. section 5.1.2

Use plate notation to make repeated structure explicit:

• Group repeating variables or subgraphs inside a plate; for image data, one plate can represent 784 pixels instead of 784 separate nodes. section 5.1.2
• Write the number of repetitions on the plate and index its elements with a subscript such as Xj for the jth pixel. section 5.1.2
• Nest plates when repeated entities contain their own repeated structure, then extend the model across the training images. section 5.1.2

Figure 5.7 A plate model representation of the causal DAG. Plates represent repeating variables, in this case 28 × 28 = 784 pixels. X_j is the j^th pixel.

The plate model shows how a causal DAG represents the 28 × 28 pixel structure of one image. section 5.1.2

How Causal AI covers it

How deep it goes

Defines grouping, repetition counts, indexing, nesting, and dataset extension, but does not develop inference procedures.

Examples

Uses MNIST and TMNIST images, 28 × 28 pixels, 784 repetitions, nested plates, and the indexed variable Xj.

What you can do after

Evaluate and understand compact causal DAG representations of repeated image variables and collections of training images.

How it connects

Connects repeated variables with directed acyclic graphs, causal models, probabilistic machine learning, and training data.

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Related concepts

• causal graphical modelconfigures · A causal graphical model is a probabilistic or structural model whose graph represents causal relationships and whose mechanisms support reasoning about interventions.
• plate modelingused by · Plate modeling is a probabilistic-model visualization technique that groups repeated variables into nested graphical substructures.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.