# On Reject and Refine Options in Multicategory Classification

arXiv: https://arxiv.org/abs/1701.02265 · HTML: https://mlsanity.com/paper/1701.02265/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2017.

## Built on by (most cited first, 9 of 9)

- [Machine Learning with a Reject Option: A survey](https://mlsanity.com/paper/2107.11277/) (2021)
- [Set-valued classification -- overview via a unified framework](https://mlsanity.com/paper/2102.12318/) (2021)
- [Quantifying Deep Learning Model Uncertainty in Conformal Prediction](https://mlsanity.com/paper/2306.00876/) (2023)
- [Efficient Online Set-valued Classification with Bandit Feedback](https://mlsanity.com/paper/2405.04393/) (2024)
- [Evidential Uncertainty Sets in Deep Classifiers Using Conformal Prediction](https://mlsanity.com/paper/2406.10787/) (2024)
- [Learning to Abstain From Uninformative Data](https://mlsanity.com/paper/2309.14240/) (2023)
- [Joint Training for Selective Prediction](https://mlsanity.com/paper/2410.24029/) (2024)
- [Learning Acceptance Regions for Many Classes with Anomaly Detection](https://mlsanity.com/paper/2209.09963/) (2022)
- [Conjunction Subspaces Test for Conformal and Selective Classification](https://mlsanity.com/paper/2410.12297/) (2024)

## Abstract (arXiv)

In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is often preferred. In recent years, there has been much development for binary classification with a reject option. Yet, little progress has been made for the multicategory case. In this article, we propose margin-based multicategory classification methods with a reject option. In addition, and more importantly, we introduce a new and unique refine option for the multicategory problem, where the class of an observation is predicted to be from a set of class labels, whose cardinality is not necessarily one. The main advantage of both options lies in their capacity of identifying error-prone observations. Moreover, the refine option can provide more constructive information for classification by effectively ruling out implausible classes. Efficient implementations have been developed for the proposed methods. On the theoretical side, we offer a novel statistical learning theory and show a fast convergence rate of the excess ℓ-risk of our methods with emphasis on diverging dimensionality and number of classes. The results can be further improved under a low noise assumption. A set of comprehensive simulation and real data studies has shown the usefulness of the new learning tools compared to regular multicategory classifiers. Detailed proofs of theorems and extended numerical results are included in the supplemental materials available online.