# Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Data

arXiv: https://arxiv.org/abs/2607.08103 · HTML: https://mlsanity.com/paper/2607.08103/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 62 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Builds on (most cited first, 26 of 26)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [Peer Loss Functions: Learning from Noisy Labels without Knowing Noise Rates](https://mlsanity.com/paper/1910.03231/) (2019)
- [Learning From Noisy Labels By Regularized Estimation Of Annotator Confusion](https://mlsanity.com/paper/1902.03680/) (2019)
- [Photo Aesthetics Ranking Network with Attributes and Content Adaptation](https://mlsanity.com/paper/1606.01621/) (2016)
- [Selective-Supervised Contrastive Learning with Noisy Labels](https://mlsanity.com/paper/2203.04181/) (2022)
- [Deep Label Distribution Learning with Label Ambiguity](https://mlsanity.com/paper/1611.01731/) (2016)
- [Masking: A New Perspective of Noisy Supervision](https://mlsanity.com/paper/1805.08193/) (2018)
- [Curriculum Loss: Robust Learning and Generalization against Label Corruption](https://mlsanity.com/paper/1905.10045/) (2019)
- [Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression](https://mlsanity.com/paper/2103.13629/) (2021)
- [C-Mixup: Improving Generalization in Regression](https://mlsanity.com/paper/2210.05775/) (2022)
- [Improving Deep Regression with Ordinal Entropy](https://mlsanity.com/paper/2301.08915/) (2023)
- [Moving Window Regression: A Novel Approach to Ordinal Regression](https://mlsanity.com/paper/2203.13122/) (2022)
- [BridgeNet: A Continuity-Aware Probabilistic Network for Age Estimation](https://mlsanity.com/paper/1904.03358/) (2019)
- [Deep Regression Forests for Age Estimation](https://mlsanity.com/paper/1712.07195/) (2017)
- [Unimodal-Concentrated Loss: Fully Adaptive Label Distribution Learning for Ordinal Regression](https://mlsanity.com/paper/2204.00309/) (2022)
- [ConR: Contrastive Regularizer for Deep Imbalanced Regression](https://mlsanity.com/paper/2309.06651/) (2023)
- [Scalable Penalized Regression for Noise Detection in Learning with Noisy Labels](https://mlsanity.com/paper/2203.07788/) (2022)
- [CLOC: Contrastive Learning for Ordinal Classification with Multi-Margin N-pair Loss](https://mlsanity.com/paper/2504.17813/) (2025)
- [Robust Deep Ordinal Regression Under Label Noise](https://mlsanity.com/paper/1912.03488/) (2019)
- [Sample Selection via Contrastive Fragmentation for Noisy Label Regression](https://mlsanity.com/paper/2502.17771/) (2025)

## Abstract (arXiv)

Rank estimation under label noise poses a fundamental challenge, as ordinal annotations often exhibit structured uncertainty rather than simple label corruption. In this paper, we reformulate rank estimation with noisy ordinal labels as a stochastic ordering problem, in which each instance is inherently associated with multiple plausible ranks instead of a single deterministic label. Based on this view, we propose stochastic order learning (SOL), a learning framework that captures ordinal label uncertainty and learns an embedding space through two complementary objectives: a discriminative loss that structures instance--centroid interactions and a stochastic order loss that enforces probabilistic ordering relations between instances. Extensive experiments across diverse datasets demonstrate that SOL enables reliable rank estimation under various types and levels of label noise. The source code is available at https://github.com/cwlee00/SOL.