有序多类ROC超曲面下体积的快速无偏估计

Fast and Unbiased Estimation of Volume under Ordered Multi-Class ROC Hyper-Surface (VUHS) with Discrete Measurements

摘要: 接收机工作特性曲线(ROC)分析在科学和工程领域中特别时在机器学习中处理二分类问题时被广泛应用。然而，在实际情况下，多分类问题常常出现。为解决这个问题，学者引入了多类ROC超曲面下的体积VUHS概念，尽管已有学者提出了连续样本下计算VUHS的快速算法，但对离散样本下的VUHS研究仍显不足。本文提出了一种新的方法：基于动态规划(DP)的VUHS快速无偏估计算法。该算法旨在提高计算效率并确保无偏性，可同时处理连续及离散母体样本下的问题。通过实验验证了该算法的无偏性和计算效率，证实了其在处理多分类问题中的有效性和可靠性。

Abstract: Receiver Operating Characteristic (ROC) analysis is extensively utilized in scientific and engineering domains, particularly when dealing with binary classification problems in machine learning. However, multiclass classification issues frequently arise in practical scenarios. To tackle this issue, scholars have introduced the concept of the Volume under the Hypersurface of the multi-class ROC (VUHS); although fast algorithms for computing VUHS have been proposed under continuous sample distributions, research on VUHS for discrete sample cases remains insufficient. This paper presents a novel approach: a Fast and Unbiased Estimation Algorithm for VUHS based on Dynamic Programming (DP). This algorithm aims to enhance computational efficiency while ensuring unbiasedness, capable of addressing problems derived from both continuous and discrete parent populations. The experimental validation confirms the algorithm’s unbiasedness and computational efficiency, substantiating its effectiveness and reliability in handling multiclass classification problems.