# Explaining Reject Options of Learning Vector Quantization Classifiers

arXiv: https://arxiv.org/abs/2202.07244 · HTML: https://mlsanity.com/paper/2202.07244/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 51 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 14 of 14)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Deep Reinforcement Learning framework for Autonomous Driving](https://mlsanity.com/paper/1704.02532/) (2017)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Explainable Artificial Intelligence: Understanding, Visualizing and Interpreting Deep Learning Models](https://mlsanity.com/paper/1708.08296/) (2017)
- [Convex Density Constraints for Computing Plausible Counterfactual Explanations](https://mlsanity.com/paper/2002.04862/) (2020)
- [A review of learning vector quantization classifiers](https://mlsanity.com/paper/1509.07093/) (2015)
- [Examining Deep Learning Architectures for Crime Classification and Prediction](https://mlsanity.com/paper/1812.00602/) (2018)
- [Convex optimization for actionable & plausible counterfactual explanations](https://mlsanity.com/paper/2105.07630/) (2021)
- [Optimum Reject Options for Prototype-based Classification](https://mlsanity.com/paper/1503.06549/) (2015)

## Built on by (most cited first, 7 of 7)

- ["Even if ..." -- Diverse Semifactual Explanations of Reject](https://mlsanity.com/paper/2207.01898/) (2022)
- [Model Agnostic Local Explanations of Reject](https://mlsanity.com/paper/2205.07623/) (2022)
- [Interpretable and Fair Mechanisms for Abstaining Classifiers](https://mlsanity.com/paper/2503.18826/) (2025)
- [Precision and Recall Reject Curves for Classification](https://mlsanity.com/paper/2308.08381/) (2023)
- [Model Agnostic Explainable Selective Regression via Uncertainty Estimation](https://mlsanity.com/paper/2311.09145/) (2023)
- [Stacked Confusion Reject Plots (SCORE)](https://mlsanity.com/paper/2406.17346/) (2024)
- [Concisely Explaining the Doubt: Minimum-Size Abductive Explanations for Linear Models with a Reject Option](https://mlsanity.com/paper/2603.14096/) (2026)

## Abstract (arXiv)

While machine learning models are usually assumed to always output a prediction, there also exist extensions in the form of reject options which allow the model to reject inputs where only a prediction with an unacceptably low certainty would be possible. With the ongoing rise of eXplainable AI, a lot of methods for explaining model predictions have been developed. However, understanding why a given input was rejected, instead of being classified by the model, is also of interest. Surprisingly, explanations of rejects have not been considered so far. We propose to use counterfactual explanations for explaining rejects and investigate how to efficiently compute counterfactual explanations of different reject options for an important class of models, namely prototype-based classifiers such as learning vector quantization models.