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 in training both linear models and deep neural networks for partial AUC maximization and sum of ranked range loss minimization.

Fairness metrics utilizing the area under the receiver operator characteristic curve (AUC) have gained increasing attention in high-stakes domains such as healthcare, finance, and criminal justice. In these domains, fairness is often evaluated over risk scores rather than binary outcomes, and a common challenge is that enforcing strict fairness can significantly degrade AUC performance. To address this challenge, we propose Fair Proportional Optimal Transport (FairPOT), a novel, model-agnostic post-processing framework that strategically aligns risk score distributions across different groups using optimal transport, but does so selectively by transforming a controllable proportion, i.e., the top-lambda quantile, of scores within the disadvantaged group. By varying lambda, our method allows for a tunable trade-off between reducing AUC disparities and maintaining overall AUC performance. Furthermore, we extend FairPOT to the partial AUC setting, enabling fairness interventions to concentrate on the highest-risk regions. Extensive experiments on synthetic, public, and clinical datasets show that FairPOT consistently outperforms existing post-processing techniques in both global and partial AUC scenarios, often achieving improved fairness with slight AUC degradation or even positive gains in utility. The computational efficiency and practical adaptability of FairPOT make it a promising solution for real-world deployment.

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.

Optimization metrics are crucial for building recommendation systems at scale. However, an effective and efficient metric for practical use remains elusive. While Top-K ranking metrics are the gold standard for optimization, they suffer from significant computational overhead. Alternatively, the more efficient accuracy and AUC metrics often fall short of capturing the true targets of recommendation tasks, leading to suboptimal performance. To overcome this dilemma, we propose a new optimization metric, Lower-Left Partial AUC (LLPAUC), which is computationally efficient like AUC but strongly correlates with Top-K ranking metrics. Compared to AUC, LLPAUC considers only the partial area under the ROC curve in the Lower-Left corner to push the optimization focus on Top-K. We provide theoretical validation of the correlation between LLPAUC and Top-K ranking metrics and demonstrate its robustness to noisy user feedback. We further design an efficient point-wise recommendation loss to maximize LLPAUC and evaluate it on three datasets, validating its effectiveness and robustness.

Since acquiring perfect supervision is usually difficult, real-world machine learning tasks often confront inaccurate, incomplete, or inexact supervision, collectively referred to as weak supervision. In this work, we present WSAUC, a unified framework for weakly supervised AUC optimization problems, which covers noisy label learning, positive-unlabeled learning, multi-instance learning, and semi-supervised learning scenarios. Within the WSAUC framework, we first frame the AUC optimization problems in various weakly supervised scenarios as a common formulation of minimizing the AUC risk on contaminated sets, and demonstrate that the empirical risk minimization problems are consistent with the true AUC. Then, we introduce a new type of partial AUC, specifically, the reversed partial AUC (rpAUC), which serves as a robust training objective for AUC maximization in the presence of contaminated labels. WSAUC offers a universal solution for AUC optimization in various weakly supervised scenarios by maximizing the empirical rpAUC. Theoretical and experimental results under multiple settings support the effectiveness of WSAUC on a range of weakly supervised AUC optimization tasks.

Researchers from all over the world contribute to this repository as a prelude to the peer review process for publication in traditional journals. The articles listed below represent a small fraction of all articles appearing on the preprint server. They are listed in no particular order with a link to each paper along with a brief overview. Links to GitHub repos are provided when available. Especially relevant articles are marked with a "thumbs up" icon.

Optimal performance is critical for decision-making tasks from medicine to autonomous driving, however common performance measures may be too general or too specific. For binary classifiers, diagnostic tests or prognosis at a timepoint, measures such as the area under the receiver operating characteristic curve, or the area under the precision recall curve, are too general because they include unrealistic decision thresholds. On the other hand, measures such as accuracy, sensitivity or the F1 score are measures at a single threshold that reflect an individual single probability or predicted risk, rather than a range of individuals or risk. We propose a method in between, deep ROC analysis, that examines groups of probabilities or predicted risks for more insightful analysis. We translate esoteric measures into familiar terms: AUC and the normalized concordant partial AUC are balanced average accuracy (a new finding); the normalized partial AUC is average sensitivity; and the normalized horizontal partial AUC is average specificity. Along with post-test measures, we provide a method that can improve model selection in some cases and provide interpretation and assurance for patients in each risk group. We demonstrate deep ROC analysis in two case studies and provide a toolkit in Python.

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 \emph{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.