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Multiclass Classification with Rare Useful Features: Fundamental Limits and the Optimality of Diversity Pursuit Higher Criticism

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Learning from unlabeled and positive-unlabeled data

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Studies multiclass classification when only a vanishing fraction of features are useful, deriving fundamental limits and showing a diversity pursuit higher criticism procedure is optimal in a rare-feature diversity model.

Problem

High-dimensional classification with many classes where only rare features are useful; in the multiclass setting a feature can be useful without separating any specific pair of classes, which the binary theory does not cover.

Approach

Extends the binary rare-useful-feature theory to multiclass via a diversity model, establishing information-theoretic limits and proposing Diversity Pursuit Higher Criticism as a feature selection procedure that attains them.

Key results

• Establishes fundamental limits for multiclass classification with rare useful features (from abstract).
• Shows Diversity Pursuit Higher Criticism is optimal in the rare feature diversity model (from abstract).

Experimental setup

Builds on: higher criticism rare-useful-feature binary classification theory

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