Paper Info
Title
Fast and unbiased estimation of volume under the ordered multi-class ROC hyper-surface with continuous measurements
Abstract
Receiver operating characteristic (ROC) analysis is a popular tool to deal with two-class problems in many science and engineering areas. However, in practice, multi-class problems are frequently encountered, such as in ordinal regression in the area of machine learning. The volume under the multi-class ROC hyper-surface (VUHS) has been proposed to evaluate the performance of multi-class classifiers. Unfortunately, however, the computational loads of current methods are rather heavy, making them impracticable in scenarios where the sample size is large. Moreover, the null distribution, which is mandatory for significance test, is also unknown to the best of our knowledge. To improve such unsatisfactory situations, in this article we develop an efficient algorithm for unbiased estimation of VUHS and the corresponding variance. Exploiting the technique of dynamic programming (DP) as well as Dyck paths, our proposed algorithm outperforms the state-of-the-art algorithm based on graph theoretic for large samples. In addition, we derive the analytical expressions of the mean and variance of VUHS under the null distribution. Theoretical analysis and Monte Carlo simulations verified both the unbiasedness and computational efficiency of our algorithm. (C) 2022 Elsevier Inc. All rights reserved.
Year
DOI
Venue
2022
10.1016/j.dsp.2022.103500
DIGITAL SIGNAL PROCESSING
Keywords
DocType
Volume
Receiver operating characteristic (ROC), Volume under the ROC hyper-surfaces (VUHS), Dynamic programming (DP), Dyck path (DKP), Null distribution
Journal
126
ISSN
Citations 
PageRank 
1051-2004
0
0.34
References 
Authors
0
5
Name
Order
Citations
PageRank
Hongbin Zhu100.34
Shun Liu202.03
Weichao Xu300.34
Changrun Chen401.69
Hua Tan500.34