# Support Vector Algorithms for Optimizing the Partial Area Under the ROC Curve

arXiv: https://arxiv.org/abs/1605.04337 · HTML: https://mlsanity.com/paper/1605.04337/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2016.

## Built on by (most cited first, 12 of 12)

- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Learning with Multiclass AUC: Theory and Algorithms](https://mlsanity.com/paper/2107.13171/) (2021)
- [When AUC meets DRO: Optimizing Partial AUC for Deep Learning with Non-Convex Convergence Guarantee](https://mlsanity.com/paper/2203.00176/) (2022)
- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Minimax AUC Fairness: Efficient Algorithm with Provable Convergence](https://mlsanity.com/paper/2208.10451/) (2022)
- [Large-scale Optimization of Partial AUC in a Range of False Positive Rates](https://mlsanity.com/paper/2203.01505/) (2022)
- [Optimizing Two-way Partial AUC with an End-to-end Framework](https://mlsanity.com/paper/2206.11655/) (2022)
- [Optimizing Partial Area Under the Top-k Curve: Theory and Practice](https://mlsanity.com/paper/2209.01398/) (2022)
- [Lower-Left Partial AUC: An Effective and Efficient Optimization Metric for Recommendation](https://mlsanity.com/paper/2403.00844/) (2024)
- [Asymptotically Unbiased Instance-wise Regularized Partial AUC Optimization: Theory and Algorithm](https://mlsanity.com/paper/2210.03967/) (2022)
- [Performances of Symmetric Loss for Private Data from Exponential Mechanism](https://mlsanity.com/paper/2210.04132/) (2022)
- [Closing the Approximation Gap of Partial AUC Optimization: A Tale of Two Formulations](https://mlsanity.com/paper/2512.01213/) (2025)

## Abstract (arXiv)

The area under the ROC curve (AUC) is a widely used performance measure in machine learning. Increasingly, however, in several applications, ranging from ranking to biometric screening to medicine, performance is measured not in terms of the full area under the ROC curve, but in terms of the partial area under the ROC curve between two false positive rates. In this paper, we develop support vector algorithms for directly optimizing the partial AUC between any two false positive rates. Our methods are based on minimizing a suitable proxy or surrogate objective for the partial AUC error. In the case of the full AUC, one can readily construct and optimize convex surrogates by expressing the performance measure as a summation of pairwise terms. The partial AUC, on the other hand, does not admit such a simple decomposable structure, making it more challenging to design and optimize (tight) convex surrogates for this measure. Our approach builds on the structural SVM framework of Joachims (2005) to design convex surrogates for partial AUC, and solves the resulting optimization problem using a cutting plane solver. Unlike the full AUC, where the combinatorial optimization needed in each iteration of the cutting plane solver can be decomposed and solved efficiently, the corresponding problem for the partial AUC is harder to decompose. One of our main contributions is a polynomial time algorithm for solving the combinatorial optimization problem associated with partial AUC. We also develop an approach for optimizing a tighter non-convex hinge loss based surrogate for the partial AUC using difference-of-convex programming. Our experiments on a variety of real-world and benchmark tasks confirm the efficacy of the proposed methods.