Ranking and Complex Prediction Problems

From an Instance to a Category

Many prediction tasks begin with an instance and end with a category. A document may need a topic label, or an image may need an object label. When the possible answer is one of several categories, the task is called multiclass classification. The central question is which category from the available set should be assigned to the instance.

Tracing the Prediction Inputs

Begin by separating the two sides of the task. The instance space X contains the possible inputs to the prediction. The target set Y contains the available target categories, and Y is finite. These collections are not the same kind of thing: X is the input side, while Y is the set of possible outputs.

Reading the Predictor h : X → Y

The formal goal is to learn a predictor h : X → Y. Read this as a rule that takes an instance from X and produces a target class from Y. The notation emphasizes the direction of the prediction: the input comes from the instance space, and the result belongs to the finite target set.

Tracing a Document Categorization

The important separation is between the document collection and the topic collection. Documents are instances; topics are target categories. Treating both collections as if they were the same kind of object hides the direction of the prediction.

Why One Class Is Assigned

The word multiclass matters because the target set contains several possible categories. The prediction task must choose which available category is assigned to the current instance. Thus, the same structure combines two ideas: there are multiple possible target classes, and the instance receives one choice from that set.

Common Interpretation Mistakes

• Treating X and Y as the same collection.

  X contains instances, while Y is the finite set of target categories.

  Fix: Ask first whether an item is an input instance or a possible output category.

• Reading h : X → Y as if h produced an item outside Y.

  The formal goal is a predictor from X to Y, so its output is a target class in Y.

  Fix: Trace the notation from left to right: an instance from X is mapped to a class from Y.

• Forgetting that the task has several possible target classes.

  Multiclass classification is classification into one of several possible target classes.

  Fix: Name the finite set of possible target categories before describing the assigned class.

• Assuming the example's instances and categories are interchangeable.

  The source structure distinguishes the input side from the output side.

  Fix: Label documents or images as instances and topics or object labels as target categories.

Check Your Understanding

Essential Takeaways

1. Multiclass classification assigns an instance to one of several possible target classes.
2. X is the instance space: it contains the possible inputs, such as documents or images.
3. Y is a finite set of target categories, such as topics or object labels.
4. The predictor h : X → Y maps an instance from X to a target class from Y.
5. The input collection and the target-category collection have different roles and should not be treated as the same kind of thing.