# Learning from Similarity-Confidence Data

arXiv: https://arxiv.org/abs/2102.06879 · HTML: https://mlsanity.com/paper/2102.06879/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 79 references that are in the map.
- First posted on arXiv 13 Feb 2021.

## Builds on (most cited first, 25 of 25)

- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [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)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Progressive Identification of True Labels for Partial-Label Learning](https://mlsanity.com/paper/2002.08053/) (2020)
- [Multi-class Classification without Multi-class Labels](https://mlsanity.com/paper/1901.00544/) (2019)
- [Learning with Biased Complementary Labels](https://mlsanity.com/paper/1711.09535/) (2017)
- [Masking: A New Perspective of Noisy Supervision](https://mlsanity.com/paper/1805.08193/) (2018)
- [Provably Consistent Partial-Label Learning](https://mlsanity.com/paper/2007.08929/) (2020)
- [Learning from Complementary Labels](https://mlsanity.com/paper/1705.07541/) (2017)
- [Complementary-Label Learning for Arbitrary Losses and Models](https://mlsanity.com/paper/1810.04327/) (2018)
- [Learning with Multiple Complementary Labels](https://mlsanity.com/paper/1912.12927/) (2019)
- [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)
- [Unbiased Risk Estimators Can Mislead: A Case Study of Learning with Complementary Labels](https://mlsanity.com/paper/2007.02235/) (2020)
- [Classification from Pairwise Similarities/Dissimilarities and Unlabeled Data via Empirical Risk Minimization](https://mlsanity.com/paper/1904.11717/) (2019)
- [Bridging Ordinary-Label Learning and Complementary-Label Learning](https://mlsanity.com/paper/2002.02158/) (2020)
- [Efficient Training for Positive Unlabeled Learning](https://mlsanity.com/paper/1608.06807/) (2016)
- [Multi-Class Classification from Noisy-Similarity-Labeled Data](https://mlsanity.com/paper/2002.06508/) (2020)

## Built on by (most cited first, 19 of 19)

- [Binary Classification with Confidence Difference](https://mlsanity.com/paper/2310.05632/) (2023)
- [Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practical](https://mlsanity.com/paper/2311.15502/) (2023)
- [Learning with Proper Partial Labels](https://mlsanity.com/paper/2112.12303/) (2021)
- [A General Framework for Learning from Weak Supervision](https://mlsanity.com/paper/2402.01922/) (2024)
- [A Universal Unbiased Method for Classification from Aggregate Observations](https://mlsanity.com/paper/2306.11343/) (2023)
- [Unified Risk Analysis for Weakly Supervised Learning](https://mlsanity.com/paper/2309.08216/) (2023)
- [Multi-Class Classification from Single-Class Data with Confidences](https://mlsanity.com/paper/2106.08864/) (2021)
- [Learning from Concealed Labels](https://mlsanity.com/paper/2412.02230/) (2024)
- [Learning from M-Tuple Dominant Positive and Unlabeled Data](https://mlsanity.com/paper/2506.15686/) (2025)
- [A Unified Empirical Risk Minimization Framework for Flexible N-Tuples Weak Supervision](https://mlsanity.com/paper/2507.07771/) (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)
- [Learning from Uncertain Similarity and Unlabeled Data](https://mlsanity.com/paper/2509.11984/) (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)
- [Risk-Consistent Multiclass Learning from Random Label-Subset Membership Queries](https://mlsanity.com/paper/2605.07413/) (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)

Weakly supervised learning has drawn considerable attention recently to reduce the expensive time and labor consumption of labeling massive data. In this paper, we investigate a novel weakly supervised learning problem of learning from similarity-confidence (Sconf) data, where we aim to learn an effective binary classifier from only unlabeled data pairs equipped with confidence that illustrates their degree of similarity (two examples are similar if they belong to the same class). To solve this problem, we propose an unbiased estimator of the classification risk that can be calculated from only Sconf data and show that the estimation error bound achieves the optimal convergence rate. To alleviate potential overfitting when flexible models are used, we further employ a risk correction scheme on the proposed risk estimator. Experimental results demonstrate the effectiveness of the proposed methods.