# Binary Classification with Confidence Difference

arXiv: https://arxiv.org/abs/2310.05632 · HTML: https://mlsanity.com/paper/2310.05632/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 73 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Data Programming: Creating Large Training Sets, Quickly](https://mlsanity.com/paper/1605.07723/) (2016)
- [Does label smoothing mitigate label noise?](https://mlsanity.com/paper/2003.02819/) (2020)
- [Bag of Tricks for Adversarial Training](https://mlsanity.com/paper/2010.00467/) (2020)
- [Deep learning with noisy labels: exploring techniques and remedies in medical image analysis](https://mlsanity.com/paper/1912.02911/) (2019)
- [Towards Understanding Knowledge Distillation](https://mlsanity.com/paper/2105.13093/) (2021)
- [KuaiRec: A Fully-observed Dataset and Insights for Evaluating Recommender Systems](https://mlsanity.com/paper/2202.10842/) (2022)
- [MoPro: Webly Supervised Learning with Momentum Prototypes](https://mlsanity.com/paper/2009.07995/) (2020)
- [Leveraged Weighted Loss for Partial Label Learning](https://mlsanity.com/paper/2106.05731/) (2021)
- [On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Data](https://mlsanity.com/paper/1808.10585/) (2018)
- [Eliciting and Learning with Soft Labels from Every Annotator](https://mlsanity.com/paper/2207.00810/) (2022)
- [Classification from Pairwise Similarity and Unlabeled Data](https://mlsanity.com/paper/1802.04381/) (2018)
- [Mitigating Overfitting in Supervised Classification from Two Unlabeled Datasets: A Consistent Risk Correction Approach](https://mlsanity.com/paper/1910.08974/) (2019)

## Built on by (most cited first, 13 of 13)

- [Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practical](https://mlsanity.com/paper/2311.15502/) (2023)
- [A General Framework for Learning from Weak Supervision](https://mlsanity.com/paper/2402.01922/) (2024)
- [Data-Driven Estimation of the False Positive Rate of the Bayes Binary Classifier via Soft Labels](https://mlsanity.com/paper/2401.15500/) (2024)
- [Rethinking Consistent Multi-Label Classification Under Inexact Supervision](https://mlsanity.com/paper/2510.04091/) (2025)
- [Learning from M-Tuple Dominant Positive and Unlabeled Data](https://mlsanity.com/paper/2506.15686/) (2025)
- [Learning from Hard Labels with Additional Supervision on Non-Hard-Labeled Classes](https://mlsanity.com/paper/2507.18098/) (2025)
- [Learning from Similarity-Confidence and Confidence-Difference](https://mlsanity.com/paper/2508.05108/) (2025)
- [Investigating ECG Diagnosis with Ambiguous Labels using Partial Label Learning](https://mlsanity.com/paper/2512.11095/) (2025)
- [FastBUS: A Fast Bayesian Framework for Unified Weakly-Supervised Learning](https://mlsanity.com/paper/2603.00517/) (2026)
- [Binary Classification from Coupled Pairwise Labels](https://mlsanity.com/paper/2603.19713/) (2026)
- [Embracing Biased Transition Matrices for Complementary-Label Learning with Many Classes](https://mlsanity.com/paper/2605.15586/) (2026)
- [Recent advances in weakly supervised learning: New supervision paradigms, assumption relaxations, and practical solutions](https://mlsanity.com/paper/2608.06896/) (2026)
- [AUC Maximization from Biased Positive-unlabeled Data with Confidence](https://mlsanity.com/paper/2609.10928/) (2026)

## Abstract (arXiv)

Recently, learning with soft labels has been shown to achieve better performance than learning with hard labels in terms of model generalization, calibration, and robustness. However, collecting pointwise labeling confidence for all training examples can be challenging and time-consuming in real-world scenarios. This paper delves into a novel weakly supervised binary classification problem called confidence-difference (ConfDiff) classification. Instead of pointwise labeling confidence, we are given only unlabeled data pairs with confidence difference that specifies the difference in the probabilities of being positive. We propose a risk-consistent approach to tackle this problem and show that the estimation error bound achieves the optimal convergence rate. We also introduce a risk correction approach to mitigate overfitting problems, whose consistency and convergence rate are also proven. Extensive experiments on benchmark data sets and a real-world recommender system data set validate the effectiveness of our proposed approaches in exploiting the supervision information of the confidence difference.