Large-scale Optimization of Partial AUC in a Range of False Positive Rates

Yao Yao; Qihang Lin; Tianbao Yang

doi:10.48550/arxiv.2203.01505

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Large-scale Optimization of Partial AUC in a Range of False Positive Rates

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Large-scale Optimization of Partial AUC in a Range of False Positive Rates

Yao Yao, Qihang Lin and Tianbao Yang

ArXiv.org

03/02/2022

DOI: 10.48550/arxiv.2203.01505

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. However, it summarizes the true positive rates (TPRs) over all false positive rates (FPRs) in the ROC space, which may include the FPRs with no practical relevance in some applications. The partial AUC, as a generalization of the AUC, summarizes only the TPRs over a specific range of the FPRs and is thus a more suitable performance measure in many real-world situations. Although partial AUC optimization in a range of FPRs had been studied, existing algorithms are not scalable to big data and not applicable to deep learning. To address this challenge, we cast the problem into a non-smooth difference-of-convex (DC) program for any smooth predictive functions (e.g., deep neural networks), which allowed us to develop an efficient approximated gradient descent method based on the Moreau envelope smoothing technique, inspired by recent advances in non-smooth DC optimization. To increase the efficiency of large data processing, we used an efficient stochastic block coordinate update in our algorithm. Our proposed algorithm can also be used to minimize the sum of ranked range loss, which also lacks efficient solvers. We established a complexity of $\tilde O(1/\epsilon^6)$ for finding a nearly $\epsilon$-critical solution. Finally, we numerically demonstrated the effectiveness of our proposed algorithms for both partial AUC maximization and sum of ranked range loss minimization.

Details

Title: Subtitle: Large-scale Optimization of Partial AUC in a Range of False Positive Rates
Creators: Yao Yao
Qihang Lin
Tianbao Yang
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2203.01505
ISSN: 2331-8422
Language: English
Date posted: 03/02/2022
Academic Unit: Business Analytics; Computer Science
Record Identifier: 9984380701002771

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