[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85054-en":3,"doc-seo-85054-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85054,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Stochastic Order Learning An Approach to Rank Estimation Using Noisy Data","Rank estimation under label noise addresses ordinal uncertainty that is structured rather than simple corruption. The paper reformulates rank estimation with noisy ordinal labels as a stochastic ordering problem, treating each instance as linked to multiple plausible ranks instead of one deterministic label. It introduces stochastic order learning (SOL), which learns an embedding space using two complementary objectives: an interaction-structuring discriminative loss and a probabilistic stochastic order loss. Experiments across diverse datasets show reliable performance under varied noise types and intensities.","Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Data  \nChaewon Lee 1 Seon-Ho Lee 2 Chang-Su Kim 1  \narXiv :2607 .08 103v 1 [ cs .LG] 9 Jul 2026  \nAbstract  \nRank 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](https://github.com/cwlee00/SOL).  \n1. Introduction  \nRank estimation—a task to predict the rank or ‘ordered class’ of an object—is a fundamental problem in machine learning, with applications including facial age estimation (Ricanek & Tesafaye, 2006 ; Shin et al., 2022), aesthetic score regression (Kong et al., 2016), and medical assessment (Halabi et al., 2019) . In practice, however, obtaining error-free ordinal annotations is challenging, as distinctions between adjacent labels are often subtle. For instance, facial appearance changes little over short age gaps, making annotation errors inevitable; indeed, Escalera et al. (2015) showed that apparent age distributions differ from real ages. Label noise also arises from subjectivity, as in aesthetic assessment where no universal scoring criterion exists, and from inter-observer variability in medical image analysis  \n1 School of Electrical Engineering, Korea University, Seoul, Korea 2Amazon AGI, Seattle, USA. Correspondence to: Chang-Su Kim \u003C[changsukim@korea.ac.kr](changsukim@korea.ac.kr) >.  \nProceedings of the 43 rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026 . Copyright 2026 by the author(s) .  \n(Halabi et al., 2019) . To mitigate such variability, annotations are often aggregated by averaging estimates from multiple experts.  \nMany algorithms have been developed to train machines using imperfect data with noisy labels, but most of them are for classification (Tanno et al., 2019 ; Song et al., 2019 ; Ma et al., 2020 ; Yao et al., 2022 ; Ye et al., 2023) or segmentation (Yang et al., 2020 ; Li et al., 2023) . Unlike classification or segmentation, rank estimation suffers from varying degrees of label errors due to the ordinal property of classes. Figure 1 compares nominal data for classification and ordered data for rank estimation. In classification, misclassifying a dog as a cat is as harmful as misclassifying a dog as a bear. In contrast, in rank estimation, the error of estimating a 43-year-old as a 59-year-old is severer than that of mistaking a 24-year-old as a 26-year-old. Since noise-robust classification methods treat all noise identically, they are prone to making big estimation errors and are incapable of identifying extreme outliers when applied to ordered data.  \nAlthough several noise-robust regression methods exist, regression-based models are known to underperform compared to classification- or ranking-based methods. As pointed out by Zhang et al. (2023), direct regression may fail to learn high-entropy feature representations, resulting in lower mutual information between learned representationsand target outputs. Order learning approaches (Lim et al., 2020 ; Shin et al., 2022 ; Lee et al., 2022) overcome the limitations of direct regression and have shown promising results in rank estimation. However, these","cbCaicNR68laMCuo","https://ap.wps.com/l/cbCaicNR68laMCuo","pdf",20870126,1,32,"English","en",105,"# Introduction\n## Motivation: ordinal label noise in rank estimation\n## Limits of classification and regression approaches\n## Need for noise-robust order learning\n## Stochastic reformulation and proposed SOL framework","[{\"question\":\"What problem does the paper address in rank estimation?\",\"answer\":\"It addresses rank estimation when ordinal labels contain structured uncertainty due to annotation errors, including effects of subjectivity and inter-observer variability.\"},{\"question\":\"How does the paper reformulate rank estimation under label noise?\",\"answer\":\"It reformulates the task as a stochastic ordering problem, where each instance corresponds to multiple plausible ranks with probabilistic relationships rather than a single deterministic rank.\"},{\"question\":\"What are the core components of the proposed Stochastic Order Learning (SOL) method?\",\"answer\":\"SOL learns an embedding space using two objectives: a discriminative loss that structures instance–centroid interactions and a stochastic order loss that enforces probabilistic ordering relations between 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