# Classification from Triplet Comparison Data

arXiv: https://arxiv.org/abs/1907.10225 · HTML: https://mlsanity.com/paper/1907.10225/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 6 of 6)

- [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)
- [A Symmetric Loss Perspective of Reliable Machine Learning](https://mlsanity.com/paper/2101.01366/) (2021)
- [Reduction of Supervision for Biomedical Knowledge Discovery](https://mlsanity.com/paper/2504.09582/) (2025)
- [A Unified Empirical Risk Minimization Framework for Flexible N-Tuples Weak Supervision](https://mlsanity.com/paper/2507.07771/) (2025)
- [Learning from N-Tuple Data with M Positive Instances: Unbiased Risk Estimation and Theoretical Guarantees](https://mlsanity.com/paper/2510.18406/) (2025)

## Abstract (arXiv)

Learning from triplet comparison data has been extensively studied in the context of metric learning, where we want to learn a distance metric between two instances, and ordinal embedding, where we want to learn an embedding in an Euclidean space of the given instances that preserves the comparison order as well as possible. Unlike fully-labeled data, triplet comparison data can be collected in a more accurate and human-friendly way. Although learning from triplet comparison data has been considered in many applications, an important fundamental question of whether we can learn a classifier only from triplet comparison data has remained unanswered. In this paper, we give a positive answer to this important question by proposing an unbiased estimator for the classification risk under the empirical risk minimization framework. Since the proposed method is based on the empirical risk minimization framework, it inherently has the advantage that any surrogate loss function and any model, including neural networks, can be easily applied. Furthermore, we theoretically establish an estimation error bound for the proposed empirical risk minimizer. Finally, we provide experimental results to show that our method empirically works well and outperforms various baseline methods.