# Neyman-Pearson Multi-class Classification via Cost-sensitive Learning

arXiv: https://arxiv.org/abs/2111.04597 · HTML: https://mlsanity.com/paper/2111.04597/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 8 Nov 2021.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints](https://mlsanity.com/paper/1908.01871/) (2019)
- [Neyman-Pearson (NP) classification algorithms and NP receiver operating characteristics (NP-ROC)](https://mlsanity.com/paper/1608.03109/) (2016)
- [A Generalized Neyman-Pearson Criterion for Optimal Domain Adaptation](https://mlsanity.com/paper/1810.01545/) (2018)
- [Neyman-Pearson classification: parametrics and sample size requirement](https://mlsanity.com/paper/1802.02557/) (2018)
- [Neyman-Pearson Classification under High-Dimensional Settings](https://mlsanity.com/paper/1508.03106/) (2015)
- [Bridging Cost-sensitive and Neyman-Pearson Paradigms for Asymmetric Binary Classification](https://mlsanity.com/paper/2012.14951/) (2020)
- [Intentional Control of Type I Error over Unconscious Data Distortion: a Neyman-Pearson Approach to Text Classification](https://mlsanity.com/paper/1802.02558/) (2018)
- [A flexible model-free prediction-based framework for feature ranking](https://mlsanity.com/paper/1903.05262/) (2019)

## Built on by (most cited first, 6 of 6)

- [A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems](https://mlsanity.com/paper/2407.12710/) (2024)
- [The Cost of Local and Global Fairness in Federated Learning](https://mlsanity.com/paper/2503.22762/) (2025)
- [Hierarchical Neyman-Pearson Classification for Prioritizing Severe Disease Categories in COVID-19 Patient Data](https://mlsanity.com/paper/2210.02197/) (2022)
- [Semiparametric Learning from Open-Set Label Shift Data](https://mlsanity.com/paper/2509.14522/) (2025)
- [Multi-Group Quadratic Discriminant Analysis via Projection](https://mlsanity.com/paper/2601.05415/) (2026)
- [Neyman-Pearson Classification with Indecisions: Simultaneous Control of Selective Type I and Type II Errors](https://mlsanity.com/paper/2610.04233/) (2026)

## Abstract (arXiv)

Most existing classification methods aim to minimize the overall misclassification error rate. However, in applications such as loan default prediction, different types of errors can have varying consequences. To address this asymmetry issue, two popular paradigms have been developed: the Neyman-Pearson (NP) paradigm and the cost-sensitive (CS) paradigm. Previous studies on the NP paradigm have primarily focused on the binary case, while the multi-class NP problem poses a greater challenge due to its unknown feasibility. In this work, we tackle the multi-class NP problem by establishing a connection with the CS problem via strong duality and propose two algorithms. We extend the concept of NP oracle inequalities, crucial in binary classifications, to NP oracle properties in the multi-class context. Our algorithms satisfy these NP oracle properties under certain conditions. Furthermore, we develop practical algorithms to assess the feasibility and strong duality in multi-class NP problems, which can offer practitioners the landscape of a multi-class NP problem with various target error levels. Simulations and real data studies validate the effectiveness of our algorithms. To our knowledge, this is the first study to address the multi-class NP problem with theoretical guarantees. The proposed algorithms have been implemented in the R package textttnpcs, which is available on CRAN.