Order-Constrained ROC Regression With Application to Facial Recognition

Abstract

The receiver operating characteristic (ROC) curve is widely used to assess discriminative accuracy of two groups based on a continuous score. In a variety of applications, the distributions of such scores across the two groups exhibit a stochastic ordering. Specific examples include calibrated biomarkers in medical diagnostics or the output of matching algorithms in biometric recognition. Incorporating stochastic ordering as an additional constraint into estimation can improve statistical efficiency. In this article, we consider modeling of ROC curves using both the order constraint and covariates associated with each score given that the latter (e.g., demographic characteristics of the underlying subjects) often have a substantial impact on discriminative accuracy. The proposed method is based on the indirect ROC regression approach using a location-scale model, and quadratic optimization is used to implement the order constraint. The statistical properties of the proposed order-constrained least squares estimator are studied. Based on the theoretical results developed herein, we deduce that the proposed estimator can achieve substantial reductions in mean squared error relative to its unconstrained counterpart. Simulation studies corroborate the superior performance of the proposed approach. Its practical usefulness is demonstrated in an application to face recognition data from the “Good, Bad, and Ugly” face challenge, a domain in which accounting for covariates has hardly been studied.

KEYWORDS:

• Area under the ROC curve
• Biometric matching
• Facial recognition
• Order constraint
• ROC regression
• Stochastic ordering

Supplementary Materials

Supplement to “Order-Constrained ROC Regression With Application to Facial Recognition”: The supplementary materials provide proofs of the statements herein and further technical result and derivations, as well as additional simulation results (pdf file).

Acknowledgments

The authors are greatly indebted to the editor, an associate editor, and two reviewers for a multitude of comments and suggestions which have led to various improvements of this article.

Funding

Preliminary aspects of this research were supported in part by Award No. 2019-DU-BX-0011 awarded by the National Institute of Justice, Office of Justice Programs, US Department of Justice. The opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect those of the US Department of Justice.

OrderROC.R

R code that reproduces the results of the simulation studies and the real data analysis (plain text file).