# Optimizing Partial Area Under the Top-k Curve: Theory and Practice

arXiv: https://arxiv.org/abs/2209.01398 · HTML: https://mlsanity.com/paper/2209.01398/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 88 references that are in the map.
- First posted on arXiv 3 Sep 2022.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Future Frame Prediction for Anomaly Detection -- A New Baseline](https://mlsanity.com/paper/1712.09867/) (2017)
- [Generalization bounds for deep convolutional neural networks](https://mlsanity.com/paper/1905.12600/) (2019)
- [Smooth Loss Functions for Deep Top-k Classification](https://mlsanity.com/paper/1802.07595/) (2018)
- [One-Pass AUC Optimization](https://mlsanity.com/paper/1305.1363/) (2013)
- [Loss Functions for Top-k Error: Analysis and Insights](https://mlsanity.com/paper/1512.00486/) (2015)
- [On the Consistency of Top-k Surrogate Losses](https://mlsanity.com/paper/1901.11141/) (2019)
- [Learning with Multiclass AUC: Theory and Algorithms](https://mlsanity.com/paper/2107.13171/) (2021)
- [Top-k Multiclass SVM](https://mlsanity.com/paper/1511.06683/) (2015)
- [Analysis and Optimization of Loss Functions for Multiclass, Top-k, and Multilabel Classification](https://mlsanity.com/paper/1612.03663/) (2016)
- [A Structured Prediction Approach for Label Ranking](https://mlsanity.com/paper/1807.02374/) (2018)
- [Sparse-GAN: Sparsity-constrained Generative Adversarial Network for Anomaly Detection in Retinal OCT Image](https://mlsanity.com/paper/1911.12527/) (2019)
- [Support Vector Algorithms for Optimizing the Partial Area Under the ROC Curve](https://mlsanity.com/paper/1605.04337/) (2016)
- [Mining Unfollow Behavior in Large-Scale Online Social Networks via Spatial-Temporal Interaction](https://mlsanity.com/paper/1911.07156/) (2019)
- [Ranking Median Regression: Learning to Order through Local Consensus](https://mlsanity.com/paper/1711.00070/) (2017)
- [Learning Policies for Contextual Submodular Prediction](https://mlsanity.com/paper/1305.2532/) (2013)
- [Preference rules for label ranking: Mining patterns in multi-target relations](https://mlsanity.com/paper/1903.08504/) (2019)

## Built on by (most cited first, 9 of 9)

- [Not All Diffusion Model Activations Have Been Evaluated as Discriminative Features](https://mlsanity.com/paper/2410.03558/) (2024)
- [Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning](https://mlsanity.com/paper/2304.03398/) (2023)
- [Not All Pairs are Equal: Hierarchical Learning for Average-Precision-Oriented Video Retrieval](https://mlsanity.com/paper/2407.15566/) (2024)
- [DRAUC: An Instance-wise Distributionally Robust AUC Optimization Framework](https://mlsanity.com/paper/2311.03055/) (2023)
- [Semantic Concentration for Self-Supervised Dense Representations Learning](https://mlsanity.com/paper/2509.09429/) (2025)
- [Suppress Content Shift: Better Diffusion Features via Off-the-Shelf Generation Techniques](https://mlsanity.com/paper/2410.06719/) (2024)
- [ACES: Who Tests the Tests? Leave-One-Out AUC Consistency for Code Generation](https://mlsanity.com/paper/2604.03922/) (2026)
- [Top-K Pairwise Ranking: Bridging the Gap Among Ranking-Based Measures for Multi-Label Classification](https://mlsanity.com/paper/2407.06709/) (2024)
- [When Measures are Unreliable: Imperceptible Adversarial Perturbations toward Top-k Multi-Label Learning](https://mlsanity.com/paper/2309.00007/) (2023)

## Abstract (arXiv)

Top-k error has become a popular metric for large-scale classification benchmarks due to the inevitable semantic ambiguity among classes. Existing literature on top-k optimization generally focuses on the optimization method of the top-k objective, while ignoring the limitations of the metric itself. In this paper, we point out that the top-k objective lacks enough discrimination such that the induced predictions may give a totally irrelevant label a top rank. To fix this issue, we develop a novel metric named partial Area Under the top-k Curve (AUTKC). Theoretical analysis shows that AUTKC has a better discrimination ability, and its Bayes optimal score function could give a correct top-K ranking with respect to the conditional probability. This shows that AUTKC does not allow irrelevant labels to appear in the top list. Furthermore, we present an empirical surrogate risk minimization framework to optimize the proposed metric. Theoretically, we present (1) a sufficient condition for Fisher consistency of the Bayes optimal score function; (2) a generalization upper bound which is insensitive to the number of classes under a simple hyperparameter setting. Finally, the experimental results on four benchmark datasets validate the effectiveness of our proposed framework.