Coalition vector

As explained in Ensemble Methods for Machine Learning

A coalition vector is a binary vector indicating which features belong to a selected coalition.

A coalition vector is a binary vector that records which features participate in a SHAP coalition. A 1 keeps a feature’s value from the example being explained; a 0 replaces it with a value from another randomly selected example. section 9.4.2

SHAP uses the vector to construct surrogate examples:

• Generate a random 0–1 vector z. section 9.4.2
• For every 1, retain the corresponding feature from the original example. section 9.4.2
• For every 0, substitute that feature from another randomly selected example, producing a realistic patchwork surrogate. section 9.4.2

Five-feature example

For x = [x1, x2, x3, x4, x5], z = [1,1,0,0,1] selects the first, second, and fifth features. The mapped surrogate is x′ = [x1, x2, x3rand, x4rand, x5]. section 9.4.2

Figure 9.18 SHAP creates a surrogate training set of examples in the locality of the example whose prediction needs to be explained.

Shows how SHAP generates a surrogate training set near the example whose prediction is being explained. section 9.4.2

How Ensemble Methods for Machine Learning covers it

How deep it goes

Explains binary encoding and feature substitution step by step, then connects coalitions to the Shapley kernel.

Examples

Uses z = [1,1,0,0,1] to create a five-feature patchwork from an explained example and a random example.

What it assumes

Assumes familiarity with features, examples, black-box models, and LIME while explaining coalition construction directly.

What you can do after

Understand how SHAP turns feature coalitions into surrogate inputs for local explanations.

How it connects

Connects coalition vectors to SHAP, LIME, surrogate models, Shapley values, and the Shapley kernel.

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Related concepts

• vectorkind of · A vector is an ordered collection of components representing an element of a vector space.
• vectorkind of · A vector is an ordered, indexed sequence of elements, often numerical, represented as a mathematical quantity or a computational collection.

This explainer was generated by Manning's knowledge graph from the text of Ensemble Methods for Machine Learning. The section links point to the parts of the book it draws on.